ParallelGeneralGraph¶

ParallelGeneralGraph for parallel directed graphs (DiGraph) module

`ParallelGeneralGraph`	Class ParallelGeneralGraph for parallel implementation of directed graphs (DiGraph).
`ParallelGeneralGraph.measure_iteration`	Inner iteration for parallel measures, to update shared dictionary.
`ParallelGeneralGraph.measure_processes`	Division of total number of nodes in chuncks and parallel distribution of tasks into processes, for different kernel measure functions.
`ParallelGeneralGraph.floyd_warshall_predecessor_and_distance`	Parallel Floyd Warshall’s APSP algorithm.
`ParallelGeneralGraph.dijkstra_iteration_parallel`	Parallel SSSP algorithm based on Dijkstra’s method.
`ParallelGeneralGraph.dijkstra_single_source_shortest_path`	Wrapper for parallel SSSP algorithm based on Dijkstra’s method.
`ParallelGeneralGraph.calculate_shortest_path`	Choose the most appropriate way to compute the all-pairs shortest path depending on graph size and density.
`ParallelGeneralGraph.compute_efficiency`	Efficiency calculation.
`ParallelGeneralGraph.compute_nodal_efficiency`	Nodal efficiency calculation.
`ParallelGeneralGraph.compute_local_efficiency`	Local efficiency calculation.
`ParallelGeneralGraph.shortest_path_list_iteration`	Inner iteration for parallel shortest path list calculation, to update shared list.
`ParallelGeneralGraph.compute_betweenness_centrality`	Betweenness_centrality calculation.
`ParallelGeneralGraph.compute_closeness_centrality`	Closeness_centrality calculation.
`ParallelGeneralGraph.compute_degree_centrality`	Degree centrality calculation.
`ParallelGeneralGraph.compute_indegree_centrality`	In-degree centrality calculation.
`ParallelGeneralGraph.compute_outdegree_centrality`	Out-degree centrality calculation.

class ParallelGeneralGraph[source]

Bases: grape.general_graph.GeneralGraph

Class ParallelGeneralGraph for parallel implementation of directed graphs (DiGraph).

Constructs a new graph given an input file. A DiGraph stores nodes and edges with optional data or attributes. DiGraphs hold directed edges. Nodes can be arbitrary python objects with optional key/value attributes. Edges are represented as links between nodes with optional key/value attributes.

Initialize a graph with edges, name, or graph attributes.

Parameters

incoming_graph_data (input graph (optional, default: None)) – Data to initialize graph. If None (default) an empty graph is created. The data can be an edge list, or any NetworkX graph object. If the corresponding optional Python packages are installed the data can also be a 2D NumPy array, a SciPy sparse matrix, or a PyGraphviz graph.
attr (keyword arguments, optional (default= no attributes)) – Attributes to add to graph as key=value pairs.

See also

convert

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G = nx.Graph(name="my graph")
>>> e = [(1, 2), (2, 3), (3, 4)]  # list of edges
>>> G = nx.Graph(e)

Arbitrary graph attribute pairs (key=value) may be assigned

>>> G = nx.Graph(e, day="Friday")
>>> G.graph
{'day': 'Friday'}

add_edge(u_of_edge, v_of_edge, **attr)

Add an edge between u and v.

The nodes u and v will be automatically added if they are not already in the graph.

Edge attributes can be specified with keywords or by directly accessing the edge’s attribute dictionary. See examples below.

Parameters

v_of_edge (u_of_edge,) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.
attr (keyword arguments, optional) – Edge data (or labels or objects) can be assigned using keyword arguments.

See also

add_edges_from(): add a collection of edges

Notes

Adding an edge that already exists updates the edge data.

Many NetworkX algorithms designed for weighted graphs use an edge attribute (by default weight) to hold a numerical value.

Examples

The following all add the edge e=(1, 2) to graph G:

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> e = (1, 2)
>>> G.add_edge(1, 2)  # explicit two-node form
>>> G.add_edge(*e)  # single edge as tuple of two nodes
>>> G.add_edges_from([(1, 2)])  # add edges from iterable container

Associate data to edges using keywords:

>>> G.add_edge(1, 2, weight=3)
>>> G.add_edge(1, 3, weight=7, capacity=15, length=342.7)

For non-string attribute keys, use subscript notation.

>>> G.add_edge(1, 2)
>>> G[1][2].update({0: 5})
>>> G.edges[1, 2].update({0: 5})

add_edges_from(ebunch_to_add, **attr)

Add all the edges in ebunch_to_add.

Parameters

ebunch_to_add (container of edges) – Each edge given in the container will be added to the graph. The edges must be given as 2-tuples (u, v) or 3-tuples (u, v, d) where d is a dictionary containing edge data.
attr (keyword arguments, optional) – Edge data (or labels or objects) can be assigned using keyword arguments.

See also

add_edge(): add a single edge
add_weighted_edges_from(): convenient way to add weighted edges

Notes

Adding the same edge twice has no effect but any edge data will be updated when each duplicate edge is added.

Edge attributes specified in an ebunch take precedence over attributes specified via keyword arguments.

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edges_from([(0, 1), (1, 2)])  # using a list of edge tuples
>>> e = zip(range(0, 3), range(1, 4))
>>> G.add_edges_from(e)  # Add the path graph 0-1-2-3

Associate data to edges

>>> G.add_edges_from([(1, 2), (2, 3)], weight=3)
>>> G.add_edges_from([(3, 4), (1, 4)], label="WN2898")

add_node(node_for_adding, **attr)

Add a single node node_for_adding and update node attributes.

Parameters

node_for_adding (node) – A node can be any hashable Python object except None.
attr (keyword arguments, optional) – Set or change node attributes using key=value.

See also

add_nodes_from()

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_node(1)
>>> G.add_node("Hello")
>>> K3 = nx.Graph([(0, 1), (1, 2), (2, 0)])
>>> G.add_node(K3)
>>> G.number_of_nodes()
3

Use keywords set/change node attributes:

>>> G.add_node(1, size=10)
>>> G.add_node(3, weight=0.4, UTM=("13S", 382871, 3972649))

Notes

A hashable object is one that can be used as a key in a Python dictionary. This includes strings, numbers, tuples of strings and numbers, etc.

On many platforms hashable items also include mutables such as NetworkX Graphs, though one should be careful that the hash doesn’t change on mutables.

add_nodes_from(nodes_for_adding, **attr)

Add multiple nodes.

Parameters

nodes_for_adding (iterable container) – A container of nodes (list, dict, set, etc.). OR A container of (node, attribute dict) tuples. Node attributes are updated using the attribute dict.
attr (keyword arguments, optional (default= no attributes)) – Update attributes for all nodes in nodes. Node attributes specified in nodes as a tuple take precedence over attributes specified via keyword arguments.

See also

add_node()

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_nodes_from("Hello")
>>> K3 = nx.Graph([(0, 1), (1, 2), (2, 0)])
>>> G.add_nodes_from(K3)
>>> sorted(G.nodes(), key=str)
[0, 1, 2, 'H', 'e', 'l', 'o']

Use keywords to update specific node attributes for every node.

>>> G.add_nodes_from([1, 2], size=10)
>>> G.add_nodes_from([3, 4], weight=0.4)

Use (node, attrdict) tuples to update attributes for specific nodes.

>>> G.add_nodes_from([(1, dict(size=11)), (2, {"color": "blue"})])
>>> G.nodes[1]["size"]
11
>>> H = nx.Graph()
>>> H.add_nodes_from(G.nodes(data=True))
>>> H.nodes[1]["size"]
11

add_weighted_edges_from(ebunch_to_add, weight='weight', **attr)

Add weighted edges in ebunch_to_add with specified weight attr

Parameters

ebunch_to_add (container of edges) – Each edge given in the list or container will be added to the graph. The edges must be given as 3-tuples (u, v, w) where w is a number.
weight (string, optional (default= 'weight')) – The attribute name for the edge weights to be added.
attr (keyword arguments, optional (default= no attributes)) – Edge attributes to add/update for all edges.

See also

add_edge(): add a single edge
add_edges_from(): add multiple edges

Notes

Adding the same edge twice for Graph/DiGraph simply updates the edge data. For MultiGraph/MultiDiGraph, duplicate edges are stored.

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_weighted_edges_from([(0, 1, 3.0), (1, 2, 7.5)])

adj

Graph adjacency object holding the neighbors of each node.

This object is a read-only dict-like structure with node keys and neighbor-dict values. The neighbor-dict is keyed by neighbor to the edge-data-dict. So G.adj[3][2][‘color’] = ‘blue’ sets the color of the edge (3, 2) to “blue”.

Iterating over G.adj behaves like a dict. Useful idioms include for nbr, datadict in G.adj[n].items():.

The neighbor information is also provided by subscripting the graph. So for nbr, foovalue in G[node].data(‘foo’, default=1): works.

For directed graphs, G.adj holds outgoing (successor) info.

adjacency()

Returns an iterator over (node, adjacency dict) tuples for all nodes.

For directed graphs, only outgoing neighbors/adjacencies are included.

Returns: adj_iter – An iterator over (node, adjacency dictionary) for all nodes in the graph.
Return type: iterator

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> [(n, nbrdict) for n, nbrdict in G.adjacency()]
[(0, {1: {}}), (1, {0: {}, 2: {}}), (2, {1: {}, 3: {}}), (3, {2: {}})]

adjlist_inner_dict_factory: alias of builtins.dict

adjlist_outer_dict_factory: alias of builtins.dict

property betweenness_centrality

Betweenness centrality of the graph. Returns the betweenness centrality if already stored in the nodes. Otherwise, the attribute is computed.

Returns: betweenness_centrality attribute for every node.
Return type: dict

betweenness_centrality_kernel(nodes, tot_shortest_paths_list)

Compute betweenness centrality, from shortest path list.

Parameters

nodes (list) – list of nodes for which to compute the efficiency between them and all the other nodes.
tot_shortest_paths_list (list or multiprocessing.managers.list) – list of shortest paths with at least two nodes.

Returns

between centrality dictionary keyed by node.

Return type

dict

calculate_shortest_path()[source]

Choose the most appropriate way to compute the all-pairs shortest path depending on graph size and density. For a dense graph choose Floyd Warshall algorithm. For a sparse graph choose SSSP algorithm based on Dijkstra’s method.

Note

Edge weights of the graph are taken into account in the computation.

Returns: nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target shortest path; nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target shortest path length.
Return type: dict, dict

clear()

Remove all nodes and edges from the graph.

This also removes the name, and all graph, node, and edge attributes.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.clear()
>>> list(G.nodes)
[]
>>> list(G.edges)
[]

clear_data(attributes_to_remove)

Delete attributes for all nodes in the graph.

Parameters: attributes_to_remove (list) – a list of strings with all the attributes to remove.
Raises: ValueError

clear_edges()

Remove all edges from the graph without altering nodes.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.clear_edges()
>>> list(G.nodes)
[0, 1, 2, 3]
>>> list(G.edges)
[]

property closeness_centrality

Closeness centrality of the graph. Returns the closeness centrality if already stored in the nodes. Otherwise, the attribute is computed.

Returns: closeness_centrality attribute for every node.
Return type: dict

closeness_centrality_kernel(nodes, shortest_path_length, tot_shortest_paths_list, graph_size)

Compute betweenness centrality, from shortest path list.

Parameters

nodes (list) – list of nodes for which to compute the efficiency between them and all the other nodes.
shortest_path (dict) – nested dictionary with key. corresponding to source, while as value a dictionary keyed by target and valued by the source-target shortest path.
tot_shortest_paths_list (list or multiprocessing.managers.list) – list of shortest paths with at least two nodes.
graph_size (int) – graph size.

Returns

closeness centrality dictionary keyed by node.

Return type

dict

Raises

ValueError

compute_betweenness_centrality()[source]

Betweenness_centrality calculation.

Note

Betweenness centrality is an index of the relative importance of a node and it is defined by the number of shortest paths that run through it. Nodes with the highest betweenness centrality hold the higher level of control on the information flowing between different nodes in the network, because more information will pass through them.

Returns: betweenness centrality computed for every node.
Return type: multiprocessing.managers.dict

compute_closeness_centrality()[source]

Closeness_centrality calculation.

Note

Closeness centrality measures the reciprocal of the average shortest path distance from a node to all other reachable nodes in the graph. Thus, the more central a node is, the closer it is to all other nodes. This measure allows to identify good broadcasters, that is key elements in a graph, depicting how closely the nodes are connected with each other.

Returns: closeness centrality computed for every node.
Return type: multiprocessing.managers.dict

compute_degree_centrality()[source]

Degree centrality calculation.

Note

Degree centrality is a simple centrality measure that counts how many neighbors a node has in an undirected graph. The more neighbors the node has the most important it is, occupying a strategic position that serves as a source or conduit for large volumes of flux transactions with other nodes. A node with high degree centrality is a node with many dependencies.

Returns: degree centrality computed for every node.
Return type: multiprocessing.managers.dict

compute_efficiency()[source]

Efficiency calculation.

Note

The efficiency of a path connecting two nodes is defined as the inverse of the path length, if the path has length non-zero, and zero otherwise.

Returns: efficiency computed for every node. The keys correspond to source, while as value a dictionary keyed by target and valued by the source-target efficiency.
Return type: multiprocessing.managers.dict

compute_indegree_centrality()[source]

In-degree centrality calculation.

Note

In-degree centrality is measured by the number of edges ending at the node in a directed graph. Nodes with high in-degree centrality are called cascade resulting nodes.

Returns: in-degree centrality computed for every node.
Return type: multiprocessing.managers.dict

compute_local_efficiency()[source]

Local efficiency calculation.

Note

The local efficiency shows the efficiency of the connections between the first-order outgoing neighbors of node v when v is removed. Equivalently, local efficiency measures the resilience of the digraph to the perturbation of node removal, i.e. if we remove a node, how efficiently its first-order outgoing neighbors can communicate. It is in the range [0, 1].

Returns: local efficiency computed for every node.
Return type: multiprocessing.managers.dict

compute_nodal_efficiency()[source]

Nodal efficiency calculation.

Note

The nodal efficiency of the node is equal to zero for a node without any outgoing path and equal to one if from it we can reach each node of the digraph.

Returns: nodal efficiency computed for every node.
Return type: multiprocessing.managers.dict

compute_outdegree_centrality()[source]

Out-degree centrality calculation.

Note

Out-degree centrality is measured by the number of edges starting from a node in a directed graph. Nodes with high out-degree centrality are called cascade inititing nodes.

Returns: out-degree centrality computed for every node.
Return type: multiprocessing.managers.dict

compute_service()

Compute service for every node, together with edge splitting.

Returns: computed service computed for every node; splitting computed for every edge.
Return type: dict, dict

construct_path_kernel(nodes, predecessor)

Reconstruct source-target paths starting from predecessors matrix, and populate the dictionary of shortest paths.

Parameters

nodes (list) – list of nodes for which to compute the shortest path between them and all the other nodes.
predecessor (numpy.ndarray) – matrix of predecessors, computed with Floyd Warshall APSP algorithm.

Returns

nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target shortest path.

Return type

dict

copy(as_view=False)

Returns a copy of the graph.

The copy method by default returns an independent shallow copy of the graph and attributes. That is, if an attribute is a container, that container is shared by the original an the copy. Use Python’s copy.deepcopy for new containers.

If as_view is True then a view is returned instead of a copy.

Notes

All copies reproduce the graph structure, but data attributes may be handled in different ways. There are four types of copies of a graph that people might want.

Deepcopy – A “deepcopy” copies the graph structure as well as all data attributes and any objects they might contain. The entire graph object is new so that changes in the copy do not affect the original object. (see Python’s copy.deepcopy)

Data Reference (Shallow) – For a shallow copy the graph structure is copied but the edge, node and graph attribute dicts are references to those in the original graph. This saves time and memory but could cause confusion if you change an attribute in one graph and it changes the attribute in the other. NetworkX does not provide this level of shallow copy.

Independent Shallow – This copy creates new independent attribute dicts and then does a shallow copy of the attributes. That is, any attributes that are containers are shared between the new graph and the original. This is exactly what dict.copy() provides. You can obtain this style copy using:

>>> G = nx.path_graph(5)
>>> H = G.copy()
>>> H = G.copy(as_view=False)
>>> H = nx.Graph(G)
>>> H = G.__class__(G)

Fresh Data – For fresh data, the graph structure is copied while new empty data attribute dicts are created. The resulting graph is independent of the original and it has no edge, node or graph attributes. Fresh copies are not enabled. Instead use:

>>> H = G.__class__()
>>> H.add_nodes_from(G)
>>> H.add_edges_from(G.edges)

View – Inspired by dict-views, graph-views act like read-only versions of the original graph, providing a copy of the original structure without requiring any memory for copying the information.

See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html.

Parameters: as_view (bool, optional (default=False)) – If True, the returned graph-view provides a read-only view of the original graph without actually copying any data.
Returns: G – A copy of the graph.
Return type: Graph

See also

to_directed(): return a directed copy of the graph.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> H = G.copy()

degree

A DegreeView for the Graph as G.degree or G.degree().

The node degree is the number of edges adjacent to the node. The weighted node degree is the sum of the edge weights for edges incident to that node.

This object provides an iterator for (node, degree) as well as lookup for the degree for a single node.

Parameters

nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.
weight (string or None, optional (default=None)) – The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node.

Returns

If multiple nodes are requested (the default), returns a DiDegreeView mapping nodes to their degree. If a single node is requested, returns the degree of the node as an integer.

Return type

DiDegreeView or int

See also

in_degree, out_degree

Examples

>>> G = nx.DiGraph()  # or MultiDiGraph
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.degree(0)  # node 0 with degree 1
1
>>> list(G.degree([0, 1, 2]))
[(0, 1), (1, 2), (2, 2)]

property degree_centrality

Degree centrality of the graph. Returns the degree centrality if already stored in the nodes. Otherwise, the attribute is computed.

Returns: degree_centrality attribute for every node.
Return type: dict

degree_centrality_kernel(nodes, graph_size)

Compute degree centrality.

Parameters

nodes (list) – list of nodes for which to compute the efficiency between them and all the other nodes.
graph_size (int) – graph size.

Returns

degree centrality dictionary keyed by node.

Return type

dict

Raises

ValueError

property description

description attribute for every node. :rtype: dict

Type: return

dijkstra_iteration_parallel(out_queue, nodes)[source]

Parallel SSSP algorithm based on Dijkstra’s method.

Parameters

out_queue (multiprocessing.queues.Queue) – multiprocessing queue
nodes (list) – list of starting nodes from which the SSSP should be computed to every other target node in the graph

Note

Edges weight is taken into account. Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed.

dijkstra_single_source_shortest_path()[source]

Wrapper for parallel SSSP algorithm based on Dijkstra’s method. The nested dictionaries for shortest-path, length of the paths and efficiency attributes are evaluated.

Note

Edges weight is taken into account. Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed.

Returns: nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target shortest path; nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target shortest path length.
Return type: dict, dict

edge_attr_dict_factory: alias of builtins.dict

edge_subgraph(edges)

Returns the subgraph induced by the specified edges.

The induced subgraph contains each edge in edges and each node incident to any one of those edges.

Parameters: edges (iterable) – An iterable of edges in this graph.
Returns: G – An edge-induced subgraph of this graph with the same edge attributes.
Return type: Graph

Notes

The graph, edge, and node attributes in the returned subgraph view are references to the corresponding attributes in the original graph. The view is read-only.

To create a full graph version of the subgraph with its own copy of the edge or node attributes, use:

G.edge_subgraph(edges).copy()

Examples

>>> G = nx.path_graph(5)
>>> H = G.edge_subgraph([(0, 1), (3, 4)])
>>> list(H.nodes)
[0, 1, 3, 4]
>>> list(H.edges)
[(0, 1), (3, 4)]

edges

An OutEdgeView of the DiGraph as G.edges or G.edges().

edges(self, nbunch=None, data=False, default=None)

The OutEdgeView provides set-like operations on the edge-tuples as well as edge attribute lookup. When called, it also provides an EdgeDataView object which allows control of access to edge attributes (but does not provide set-like operations). Hence, G.edges[u, v][‘color’] provides the value of the color attribute for edge (u, v) while for (u, v, c) in G.edges.data(‘color’, default=’red’): iterates through all the edges yielding the color attribute with default ‘red’ if no color attribute exists.

Parameters

nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges from these nodes.
data (string or bool, optional (default=False)) – The edge attribute returned in 3-tuple (u, v, ddict[data]). If True, return edge attribute dict in 3-tuple (u, v, ddict). If False, return 2-tuple (u, v).
default (value, optional (default=None)) – Value used for edges that don’t have the requested attribute. Only relevant if data is not True or False.

Returns

edges – A view of edge attributes, usually it iterates over (u, v) or (u, v, d) tuples of edges, but can also be used for attribute lookup as edges[u, v][‘foo’].

Return type

OutEdgeView

See also

in_edges, out_edges

Notes

Nodes in nbunch that are not in the graph will be (quietly) ignored. For directed graphs this returns the out-edges.

Examples

>>> G = nx.DiGraph()  # or MultiDiGraph, etc
>>> nx.add_path(G, [0, 1, 2])
>>> G.add_edge(2, 3, weight=5)
>>> [e for e in G.edges]
[(0, 1), (1, 2), (2, 3)]
>>> G.edges.data()  # default data is {} (empty dict)
OutEdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})])
>>> G.edges.data("weight", default=1)
OutEdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
>>> G.edges([0, 2])  # only edges originating from these nodes
OutEdgeDataView([(0, 1), (2, 3)])
>>> G.edges(0)  # only edges from node 0
OutEdgeDataView([(0, 1)])

property efficiency

Efficiency of the graph. Returns the efficiency if already stored in the nodes. Otherwise, the attribute is computed.

Returns: efficiency attribute for every node. The keys correspond to source, while as value a dictionary keyed by target and valued by the source-target efficiency.
Return type: dict

efficiency_kernel(nodes, shortest_path_length)

Compute efficiency, starting from path length attribute. Efficiency is a measure of how good is the exchange of commodities flowing from one node to the others.

Parameters

nodes (list) – list of nodes for which to compute the efficiency between them and all the other nodes.
shortest_path_length (dict) – nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target shortest path length.

Returns

nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target efficiency.

Return type

dict

property final_status

final_status attribute for switches. :rtype: dict

Type: return

floyd_warshall_initialization()

Initialization of Floyd Warshall APSP algorithm. The distancy matrix is mutuated by NetworkX graph adjacency matrix, while the predecessors matrix is initialized with node fathers. The conversion between the labels (ids) in the graph and Numpy matrix indices (and viceversa) is also exploited.

Note

In order for the ids relation to be bijective, ‘mark’ attribute must be unique for each node.

Returns: matrix of distances; matrix of predecessors.
Return type: numpy.ndarray, numpy.ndarray

floyd_warshall_kernel(distance, predecessor, init, stop, barrier=None)

Floyd Warshall’s APSP inner iteration. Distance matrix is intended to take edges weight into account.

Parameters

distance (numpy.ndarray or multiprocessing.sharedctypes.RawArray) – matrix of distances.
predecessor (numpy.ndarray or multiprocessing.sharedctypes.RawArray) – matrix of predecessors.
init (int) – starting column of numpy matrix slice.
stop (int) – ending column of numpy matrix slice.
barrier (multiprocessing.synchronize.Barrier) – multiprocessing barrier to moderate writing on distance and predecessors matrices, default to None.

floyd_warshall_predecessor_and_distance()[source]

Parallel Floyd Warshall’s APSP algorithm. The predecessors and distance matrices are evaluated, together with the nested dictionaries for shortest-path, length of the paths and efficiency attributes.

Note

Edges weight is taken into account in the distance matrix. Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed.

Returns: nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target shortest path; nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target shortest path length.
Return type: dict, dict

get_edge_data(u, v, default=None)

Returns the attribute dictionary associated with edge (u, v).

This is identical to G[u][v] except the default is returned instead of an exception if the edge doesn’t exist.

Parameters

v (u,) –
default (any Python object (default=None)) – Value to return if the edge (u, v) is not found.

Returns

edge_dict – The edge attribute dictionary.

Return type

dictionary

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G[0][1]
{}

Warning: Assigning to G[u][v] is not permitted. But it is safe to assign attributes G[u][v][‘foo’]

>>> G[0][1]["weight"] = 7
>>> G[0][1]["weight"]
7
>>> G[1][0]["weight"]
7

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.get_edge_data(0, 1)  # default edge data is {}
{}
>>> e = (0, 1)
>>> G.get_edge_data(*e)  # tuple form
{}
>>> G.get_edge_data("a", "b", default=0)  # edge not in graph, return 0
0

property global_efficiency

Average global efficiency of the whole graph.

Note

The average global efficiency of a graph is the average efficiency of all pairs of nodes.

Returns: global_efficiency attribute for every node.
Return type: float
Raises: ValueError

graph_attr_dict_factory: alias of builtins.dict

has_edge(u, v)

Returns True if the edge (u, v) is in the graph.

This is the same as v in G[u] without KeyError exceptions.

Parameters: v (u,) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.
Returns: edge_ind – True if edge is in the graph, False otherwise.
Return type: bool

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.has_edge(0, 1)  # using two nodes
True
>>> e = (0, 1)
>>> G.has_edge(*e)  #  e is a 2-tuple (u, v)
True
>>> e = (0, 1, {"weight": 7})
>>> G.has_edge(*e[:2])  # e is a 3-tuple (u, v, data_dictionary)
True

The following syntax are equivalent:

>>> G.has_edge(0, 1)
True
>>> 1 in G[0]  # though this gives KeyError if 0 not in G
True

has_node(n)

Returns True if the graph contains the node n.

Identical to n in G

Parameters: n (node) –

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.has_node(0)
True

It is more readable and simpler to use

>>> 0 in G
True

has_predecessor(u, v)

Returns True if node u has predecessor v.

This is true if graph has the edge u<-v.

has_successor(u, v)

Returns True if node u has successor v.

This is true if graph has the edge u->v.

property hubs

list of graph hubs. :rtype: list

Type: return

in_degree

An InDegreeView for (node, in_degree) or in_degree for single node.

The node in_degree is the number of edges pointing to the node. The weighted node degree is the sum of the edge weights for edges incident to that node.

This object provides an iteration over (node, in_degree) as well as lookup for the degree for a single node.

Parameters

nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.
weight (string or None, optional (default=None)) – The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node.

Returns

If a single node is requested
deg (int) – In-degree of the node
OR if multiple nodes are requested
nd_iter (iterator) – The iterator returns two-tuples of (node, in-degree).

See also

degree, out_degree

Examples

>>> G = nx.DiGraph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.in_degree(0)  # node 0 with degree 0
0
>>> list(G.in_degree([0, 1, 2]))
[(0, 0), (1, 1), (2, 1)]

in_edges

An InEdgeView of the Graph as G.in_edges or G.in_edges().

in_edges(self, nbunch=None, data=False, default=None):

Parameters

nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.
data (string or bool, optional (default=False)) – The edge attribute returned in 3-tuple (u, v, ddict[data]). If True, return edge attribute dict in 3-tuple (u, v, ddict). If False, return 2-tuple (u, v).
default (value, optional (default=None)) – Value used for edges that don’t have the requested attribute. Only relevant if data is not True or False.

Returns

in_edges – A view of edge attributes, usually it iterates over (u, v) or (u, v, d) tuples of edges, but can also be used for attribute lookup as edges[u, v][‘foo’].

Return type

InEdgeView

See also

edges

property indegree_centrality

In-degree centrality of the graph. Returns the in-degree centrality if already stored in the nodes. Otherwise, the attribute is computed.

Returns: indegree_centrality attribute for every node.
Return type: dict

indegree_centrality_kernel(nodes, graph_size)

Compute in-degree centrality.

Parameters

nodes (list) – list of nodes for which to compute the efficiency between them and all the other nodes.
graph_size (int) – graph size.

Returns

in-degree centrality dictionary keyed by node.

Return type

dict

Raises

ValueError

property init_status

init_status attribute for switches. :rtype: dict

Type: return

property initial_service

initial_service attribute for every node. :rtype: dict

Type: return

is_directed(): Returns True if graph is directed, False otherwise.

is_multigraph(): Returns True if graph is a multigraph, False otherwise.

load(filename)

Load input file. Input file must be in CSV format. Each line corresponds to a node/element description, with the relative hierarchy, together with the list of all the node attributes.

Parameters: filename (str) – input file in CSV format.
Returns: DataFrame containing the following attributes: mark, init_status, description; DataFrame containing mark and father_mark attribute.
Return type: pandas.DataFrame, pandas.DataFrame

property local_efficiency

Local efficiency of the graph. Returns the local efficiency if already stored in the nodes. Otherwise, the attribute is computed.

Returns: local_efficiency attribute for every node.
Return type: dict

local_efficiency_kernel(nodes, nodal_efficiency)

Compute local efficiency, starting from nodal efficiency attribute.

Parameters

nodes (list) – list of nodes for which to compute the efficiency between them and all the other nodes.
nodal_efficiency (dict) – nodal efficiency dictionary keyed by node.

Returns

local efficiency dictionary keyed by node.

Return type

dict

property mark

mark attribute for every node. :rtype: dict

Type: return

property mark_status

mark_status attribute for every node. :rtype: dict

Type: return

measure_iteration(nodes, record, kernel, *measure_args)[source]

Inner iteration for parallel measures, to update shared dictionary.

Parameters

nodes (list) – nodes for which to compute the shortest path between them and all the other nodes.
record (multiprocessing.managers.dict) – shared dictionary to be updated.
kernel (callable) – kernel measure to be computed.
*measure_args –
arguments for kernel measures. Have a look at specific kernel measures in GeneralGraph for the particular variables/types for each measure.

measure_processes(record, kernel, *measure_args)[source]

Division of total number of nodes in chuncks and parallel distribution of tasks into processes, for different kernel measure functions.

Parameters

record (multiprocessing.managers.dict) – shared dictionary to be updated
kernel (callable) – kernel measure to be computed
*measure_args –
arguments for kernel measures (have a look at specific kernel measures in GeneralGraph for the particular variables/types for each measure)

property name

String identifier of the graph.

This graph attribute appears in the attribute dict G.graph keyed by the string “name”. as well as an attribute (technically a property) G.name. This is entirely user controlled.

nbunch_iter(nbunch=None)

Returns an iterator over nodes contained in nbunch that are also in the graph.

The nodes in nbunch are checked for membership in the graph and if not are silently ignored.

Parameters: nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.
Returns: niter – An iterator over nodes in nbunch that are also in the graph. If nbunch is None, iterate over all nodes in the graph.
Return type: iterator
Raises: NetworkXError – If nbunch is not a node or sequence of nodes. If a node in nbunch is not hashable.

See also

Graph.__iter__()

Notes

When nbunch is an iterator, the returned iterator yields values directly from nbunch, becoming exhausted when nbunch is exhausted.

To test whether nbunch is a single node, one can use “if nbunch in self:”, even after processing with this routine.

If nbunch is not a node or a (possibly empty) sequence/iterator or None, a NetworkXError is raised. Also, if any object in nbunch is not hashable, a NetworkXError is raised.

neighbors(n)

Returns an iterator over successor nodes of n.

A successor of n is a node m such that there exists a directed edge from n to m.

Parameters: n (node) – A node in the graph
Raises: NetworkXError – If n is not in the graph.

See also

predecessors()

Notes

neighbors() and successors() are the same.

property nodal_efficiency

Nodal efficiency of the graph. Returns the nodal efficiency if already stored in the nodes. Otherwise, the attribute is computed.

Returns: nodal_efficiency attribute for every node.
Return type: dict

nodal_efficiency_kernel(nodes, efficiency, graph_size)

Compute nodal efficiency, starting from efficiency attribute.

Parameters

nodes (list) – list of nodes for which to compute the efficiency between them and all the other nodes.
efficiency (dict) – nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target efficiency.
graph_size (int) – graph size.

Returns

nodal efficiency dictionary keyed by node.

Return type

dict

Raises

ValueError

node_attr_dict_factory: alias of builtins.dict

node_dict_factory: alias of builtins.dict

nodes

A NodeView of the Graph as G.nodes or G.nodes().

Can be used as G.nodes for data lookup and for set-like operations. Can also be used as G.nodes(data=’color’, default=None) to return a NodeDataView which reports specific node data but no set operations. It presents a dict-like interface as well with G.nodes.items() iterating over (node, nodedata) 2-tuples and G.nodes[3][‘foo’] providing the value of the foo attribute for node 3. In addition, a view G.nodes.data(‘foo’) provides a dict-like interface to the foo attribute of each node. G.nodes.data(‘foo’, default=1) provides a default for nodes that do not have attribute foo.

Parameters

data (string or bool, optional (default=False)) – The node attribute returned in 2-tuple (n, ddict[data]). If True, return entire node attribute dict as (n, ddict). If False, return just the nodes n.
default (value, optional (default=None)) – Value used for nodes that don’t have the requested attribute. Only relevant if data is not True or False.

Returns

Allows set-like operations over the nodes as well as node attribute dict lookup and calling to get a NodeDataView. A NodeDataView iterates over (n, data) and has no set operations. A NodeView iterates over n and includes set operations.

When called, if data is False, an iterator over nodes. Otherwise an iterator of 2-tuples (node, attribute value) where the attribute is specified in data. If data is True then the attribute becomes the entire data dictionary.

Return type

NodeView

Notes

If your node data is not needed, it is simpler and equivalent to use the expression for n in G, or list(G).

Examples

There are two simple ways of getting a list of all nodes in the graph:

>>> G = nx.path_graph(3)
>>> list(G.nodes)
[0, 1, 2]
>>> list(G)
[0, 1, 2]

To get the node data along with the nodes:

>>> G.add_node(1, time="5pm")
>>> G.nodes[0]["foo"] = "bar"
>>> list(G.nodes(data=True))
[(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})]
>>> list(G.nodes.data())
[(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})]

>>> list(G.nodes(data="foo"))
[(0, 'bar'), (1, None), (2, None)]
>>> list(G.nodes.data("foo"))
[(0, 'bar'), (1, None), (2, None)]

>>> list(G.nodes(data="time"))
[(0, None), (1, '5pm'), (2, None)]
>>> list(G.nodes.data("time"))
[(0, None), (1, '5pm'), (2, None)]

>>> list(G.nodes(data="time", default="Not Available"))
[(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')]
>>> list(G.nodes.data("time", default="Not Available"))
[(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')]

If some of your nodes have an attribute and the rest are assumed to have a default attribute value you can create a dictionary from node/attribute pairs using the default keyword argument to guarantee the value is never None:

>>> G = nx.Graph()
>>> G.add_node(0)
>>> G.add_node(1, weight=2)
>>> G.add_node(2, weight=3)
>>> dict(G.nodes(data="weight", default=1))
{0: 1, 1: 2, 2: 3}

number_of_edges(u=None, v=None)

Returns the number of edges between two nodes.

Parameters: v (u,) – If u and v are specified, return the number of edges between u and v. Otherwise return the total number of all edges.
Returns: nedges – The number of edges in the graph. If nodes u and v are specified return the number of edges between those nodes. If the graph is directed, this only returns the number of edges from u to v.
Return type: int

See also

size()

Examples

For undirected graphs, this method counts the total number of edges in the graph:

>>> G = nx.path_graph(4)
>>> G.number_of_edges()
3

If you specify two nodes, this counts the total number of edges joining the two nodes:

>>> G.number_of_edges(0, 1)
1

For directed graphs, this method can count the total number of directed edges from u to v:

>>> G = nx.DiGraph()
>>> G.add_edge(0, 1)
>>> G.add_edge(1, 0)
>>> G.number_of_edges(0, 1)
1

number_of_nodes()

Returns the number of nodes in the graph.

Returns: nnodes – The number of nodes in the graph.
Return type: int

See also

order(): identical method
__len__(): identical method

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.number_of_nodes()
3

order()

Returns the number of nodes in the graph.

Returns: nnodes – The number of nodes in the graph.
Return type: int

See also

number_of_nodes(): identical method
__len__(): identical method

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.order()
3

out_degree

An OutDegreeView for (node, out_degree)

The node out_degree is the number of edges pointing out of the node. The weighted node degree is the sum of the edge weights for edges incident to that node.

This object provides an iterator over (node, out_degree) as well as lookup for the degree for a single node.

Parameters

nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.
weight (string or None, optional (default=None)) – The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node.

Returns

If a single node is requested
deg (int) – Out-degree of the node
OR if multiple nodes are requested
nd_iter (iterator) – The iterator returns two-tuples of (node, out-degree).

See also

degree, in_degree

Examples

>>> G = nx.DiGraph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.out_degree(0)  # node 0 with degree 1
1
>>> list(G.out_degree([0, 1, 2]))
[(0, 1), (1, 1), (2, 1)]

out_edges

An OutEdgeView of the DiGraph as G.edges or G.edges().

edges(self, nbunch=None, data=False, default=None)

The OutEdgeView provides set-like operations on the edge-tuples as well as edge attribute lookup. When called, it also provides an EdgeDataView object which allows control of access to edge attributes (but does not provide set-like operations). Hence, G.edges[u, v][‘color’] provides the value of the color attribute for edge (u, v) while for (u, v, c) in G.edges.data(‘color’, default=’red’): iterates through all the edges yielding the color attribute with default ‘red’ if no color attribute exists.

Parameters

nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges from these nodes.
data (string or bool, optional (default=False)) – The edge attribute returned in 3-tuple (u, v, ddict[data]). If True, return edge attribute dict in 3-tuple (u, v, ddict). If False, return 2-tuple (u, v).
default (value, optional (default=None)) – Value used for edges that don’t have the requested attribute. Only relevant if data is not True or False.

Returns

edges – A view of edge attributes, usually it iterates over (u, v) or (u, v, d) tuples of edges, but can also be used for attribute lookup as edges[u, v][‘foo’].

Return type

OutEdgeView

See also

in_edges, out_edges

Notes

Nodes in nbunch that are not in the graph will be (quietly) ignored. For directed graphs this returns the out-edges.

Examples

>>> G = nx.DiGraph()  # or MultiDiGraph, etc
>>> nx.add_path(G, [0, 1, 2])
>>> G.add_edge(2, 3, weight=5)
>>> [e for e in G.edges]
[(0, 1), (1, 2), (2, 3)]
>>> G.edges.data()  # default data is {} (empty dict)
OutEdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})])
>>> G.edges.data("weight", default=1)
OutEdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
>>> G.edges([0, 2])  # only edges originating from these nodes
OutEdgeDataView([(0, 1), (2, 3)])
>>> G.edges(0)  # only edges from node 0
OutEdgeDataView([(0, 1)])

property outdegree_centrality

Out-degree centrality of the graph. Returns the out-degree centrality if already stored in the nodes. Otherwise, the attribute is computed.

Returns: outdegree_centrality attribute for every node.
Return type: dict

outdegree_centrality_kernel(nodes, graph_size)

Compute out-degree centrality.

Parameters

nodes (list) – list of nodes for which to compute the efficiency between them and all the other nodes.
graph_size (int) – graph size.

Returns

out-degree dictionary keyed by node.

Return type

dict

Raises

ValueError

pred

Graph adjacency object holding the predecessors of each node.

This object is a read-only dict-like structure with node keys and neighbor-dict values. The neighbor-dict is keyed by neighbor to the edge-data-dict. So G.pred[2][3][‘color’] = ‘blue’ sets the color of the edge (3, 2) to “blue”.

Iterating over G.pred behaves like a dict. Useful idioms include for nbr, datadict in G.pred[n].items():. A data-view not provided by dicts also exists: for nbr, foovalue in G.pred[node].data(‘foo’): A default can be set via a default argument to the data method.

predecessors(n)

Returns an iterator over predecessor nodes of n.

A predecessor of n is a node m such that there exists a directed edge from m to n.

Parameters: n (node) – A node in the graph
Raises: NetworkXError – If n is not in the graph.

See also

successors()

print_graph(radius=None, initial_pos=None, fixed_nodes=None, n_iter=500, thresh=0.0001, size=800, border='black', edge_width=1.0, arrow_size=10, fsize=12, fcolor='k', title='Graph', legend=True, legend_loc='upper right', legend_ncol=1, legend_anchor=None, legend_fsize=12, save_to_file=None, status=None)

Print the graph. Positions of the nodes are generated from a spring layout simulation, if not asked to be fixed during it. Initial positions can be specified for the nodes. Both initial positions and fixed positions can be specified just for a subset of the nodes. The shapes of the nodes characterize their type (SOURCE/HUB/USER/SWITCH). The font size, family and color for labels can be also specified, together with the title for the window figure.

Parameters

radius (float, optional, default to 1/sqrt(n) where n is the number of nodes in the graph) – optimal distance between nodes.
initial_pos (dict, optional) – initial positions for nodes as a dictionary with node as keys and values as a coordinate list or tuple, default to None. If None, then use random initial positions.
fixed_nodes (list, optional) – nodes to keep fixed at initial position, default to None. ValueError raised if fixed_nodes specified and initial_pos not.
n_iter (int, optional) – maximum number of iterations taken in spring layout simulation, default to 500.
thresh (float, optional) – threshold for relative error in node position changes. The iteration stops if the error is below this threshold, default to 0.0001.
size (int, optional) – size of nodes, default to 800.
border (color, optional) – color of node borders, default to ‘black’.
edge_width (float, optional) – width of edges, default to 1.0.
arrow_size (int, optional) – size of the arrow head’s length and width, default to 10.
fsize (int, optional) – font size for text labels, default to 12.
fcolor (string, optional) – font color string for labels, default to ‘k’ (black).
title (string, optional) – title for figure window, default to ‘Graph’.
legend (bool, optional) – show the legend on/off, default to True.
legend_loc (str, optional) – the location of the legend, default to ‘upper right’.
legend_ncol (int, optional) – the number of columns that the legend has, default to 1.
legend_anchor (2-tuple, or 4-tuple of floats, optional) – box that is used to position the legend in conjunction with loc, defaults to axes.bbox (if called as a method to Axes.legend) or figure.bbox (if Figure.legend). This argument allows arbitrary placement of the legend.
legend_fsize (int, optional) – the font size of the legend. The value must be numeric, implying the size the absolute font size in points, default to 12.
save_to_file (string, optional) – name of the file where to save the graph drawing, default to None. The extension is guesses from the filename. Interactive window is rendered in any case.
status (string, optional) – include initial condition of switches in printed graph. To activate it, set it to ‘initial’, default to None.

Returns

a dictionary of positions keyed by node.

Return type

dict

Raises

ValueError

remove_edge(u, v)

Remove the edge between u and v.

Parameters: v (u,) – Remove the edge between nodes u and v.
Raises: NetworkXError – If there is not an edge between u and v.

See also

remove_edges_from(): remove a collection of edges

Examples

>>> G = nx.Graph()  # or DiGraph, etc
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.remove_edge(0, 1)
>>> e = (1, 2)
>>> G.remove_edge(*e)  # unpacks e from an edge tuple
>>> e = (2, 3, {"weight": 7})  # an edge with attribute data
>>> G.remove_edge(*e[:2])  # select first part of edge tuple

remove_edges_from(ebunch)

Remove all edges specified in ebunch.

Parameters

ebunch (list or container of edge tuples) –

Each edge given in the list or container will be removed from the graph. The edges can be:

2-tuples (u, v) edge between u and v.

3-tuples (u, v, k) where k is ignored.

See also

remove_edge(): remove a single edge

Notes

Will fail silently if an edge in ebunch is not in the graph.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> ebunch = [(1, 2), (2, 3)]
>>> G.remove_edges_from(ebunch)

remove_node(n)

Remove node n.

Removes the node n and all adjacent edges. Attempting to remove a non-existent node will raise an exception.

Parameters: n (node) – A node in the graph
Raises: NetworkXError – If n is not in the graph.

See also

remove_nodes_from()

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> list(G.edges)
[(0, 1), (1, 2)]
>>> G.remove_node(1)
>>> list(G.edges)
[]

remove_nodes_from(nodes)

Remove multiple nodes.

Parameters: nodes (iterable container) – A container of nodes (list, dict, set, etc.). If a node in the container is not in the graph it is silently ignored.

See also

remove_node()

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> e = list(G.nodes)
>>> e
[0, 1, 2]
>>> G.remove_nodes_from(e)
>>> list(G.nodes)
[]

reverse(copy=True)

Returns the reverse of the graph.

The reverse is a graph with the same nodes and edges but with the directions of the edges reversed.

Parameters: copy (bool optional (default=True)) – If True, return a new DiGraph holding the reversed edges. If False, the reverse graph is created using a view of the original graph.

property service

Computed service. Returns the computed service if already stored in the nodes. Otherwise, the attribute is computed.

Returns: service attribute for every node.
Return type: dict

property shortest_path

Shortest existing paths between all node pairs. Returns the shortest path if already stored in the nodes. Otherwise, the attribute is computed.

Returns: shortest_path attribute for every node. The keys correspond to source, while as value a dictionary keyed by target and valued by the source-target shortest path.
Return type: dict

property shortest_path_length

Shortest path length.

Returns: shortest_path_length attribute for every node. The keys correspond to source, while as value a dictionary keyed by target and valued by the source-target shortest path length.
Return type: dict

shortest_path_list_iteration(nodes, shortest_path, tot_shortest_paths_list)[source]

Inner iteration for parallel shortest path list calculation, to update shared list.

Parameters

nodes (list) – list of nodes for which to compute the shortest path between them and all the other nodes
shortest_path (dict) – nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target shortest path.
tot_shortest_paths_list (multiprocessing.managers.list) – list of shortest paths with at least two nodes

shortest_path_list_kernel(nodes, shortest_path)

Collect the shortest paths that contain at least two nodes.

Parameters

nodes (list) – list of nodes for which to compute the list of shortest paths.
shortest_path (dict) – nested dictionary with key corresponding to source, while as value a dictionary keyed by target and valued by the source-target shortest path.

Returns

list of shortest paths.

Return type

list

size(weight=None)

Returns the number of edges or total of all edge weights.

Parameters

weight (string or None, optional (default=None)) – The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1.

Returns

size – The number of edges or (if weight keyword is provided) the total weight sum.

If weight is None, returns an int. Otherwise a float (or more general numeric if the weights are more general).

Return type

numeric

See also

number_of_edges()

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.size()
3

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edge("a", "b", weight=2)
>>> G.add_edge("b", "c", weight=4)
>>> G.size()
2
>>> G.size(weight="weight")
6.0

property sources

list of graph sources. :rtype: list

Type: return

subgraph(nodes)

Returns a SubGraph view of the subgraph induced on nodes.

The induced subgraph of the graph contains the nodes in nodes and the edges between those nodes.

Parameters: nodes (list, iterable) – A container of nodes which will be iterated through once.
Returns: G – A subgraph view of the graph. The graph structure cannot be changed but node/edge attributes can and are shared with the original graph.
Return type: SubGraph View

Notes

The graph, edge and node attributes are shared with the original graph. Changes to the graph structure is ruled out by the view, but changes to attributes are reflected in the original graph.

To create a subgraph with its own copy of the edge/node attributes use: G.subgraph(nodes).copy()

For an inplace reduction of a graph to a subgraph you can remove nodes: G.remove_nodes_from([n for n in G if n not in set(nodes)])

Subgraph views are sometimes NOT what you want. In most cases where you want to do more than simply look at the induced edges, it makes more sense to just create the subgraph as its own graph with code like:

# Create a subgraph SG based on a (possibly multigraph) G
SG = G.__class__()
SG.add_nodes_from((n, G.nodes[n]) for n in largest_wcc)
if SG.is_multigraph():
    SG.add_edges_from((n, nbr, key, d)
        for n, nbrs in G.adj.items() if n in largest_wcc
        for nbr, keydict in nbrs.items() if nbr in largest_wcc
        for key, d in keydict.items())
else:
    SG.add_edges_from((n, nbr, d)
        for n, nbrs in G.adj.items() if n in largest_wcc
        for nbr, d in nbrs.items() if nbr in largest_wcc)
SG.graph.update(G.graph)

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> H = G.subgraph([0, 1, 2])
>>> list(H.edges)
[(0, 1), (1, 2)]

succ

Graph adjacency object holding the successors of each node.

This object is a read-only dict-like structure with node keys and neighbor-dict values. The neighbor-dict is keyed by neighbor to the edge-data-dict. So G.succ[3][2][‘color’] = ‘blue’ sets the color of the edge (3, 2) to “blue”.

Iterating over G.succ behaves like a dict. Useful idioms include for nbr, datadict in G.succ[n].items():. A data-view not provided by dicts also exists: for nbr, foovalue in G.succ[node].data(‘foo’): and a default can be set via a default argument to the data method.

The neighbor information is also provided by subscripting the graph. So for nbr, foovalue in G[node].data(‘foo’, default=1): works.

For directed graphs, G.adj is identical to G.succ.

successors(n)

Returns an iterator over successor nodes of n.

A successor of n is a node m such that there exists a directed edge from n to m.

Parameters: n (node) – A node in the graph
Raises: NetworkXError – If n is not in the graph.

See also

predecessors()

Notes

neighbors() and successors() are the same.

property switches

list of graph switches. :rtype: list

Type: return

to_directed(as_view=False)

Returns a directed representation of the graph.

Returns: G – A directed graph with the same name, same nodes, and with each edge (u, v, data) replaced by two directed edges (u, v, data) and (v, u, data).
Return type: DiGraph

Notes

This returns a “deepcopy” of the edge, node, and graph attributes which attempts to completely copy all of the data and references.

This is in contrast to the similar D=DiGraph(G) which returns a shallow copy of the data.

See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html.

Warning: If you have subclassed Graph to use dict-like objects in the data structure, those changes do not transfer to the DiGraph created by this method.

Examples

>>> G = nx.Graph()  # or MultiGraph, etc
>>> G.add_edge(0, 1)
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1), (1, 0)]

If already directed, return a (deep) copy

>>> G = nx.DiGraph()  # or MultiDiGraph, etc
>>> G.add_edge(0, 1)
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1)]

to_directed_class()

Returns the class to use for empty directed copies.

If you subclass the base classes, use this to designate what directed class to use for to_directed() copies.

to_undirected(reciprocal=False, as_view=False)

Returns an undirected representation of the digraph.

Parameters

reciprocal (bool (optional)) – If True only keep edges that appear in both directions in the original digraph.
as_view (bool (optional, default=False)) – If True return an undirected view of the original directed graph.

Returns

G – An undirected graph with the same name and nodes and with edge (u, v, data) if either (u, v, data) or (v, u, data) is in the digraph. If both edges exist in digraph and their edge data is different, only one edge is created with an arbitrary choice of which edge data to use. You must check and correct for this manually if desired.

Return type

Graph

See also

Graph(), copy(), add_edge(), add_edges_from()

Notes

If edges in both directions (u, v) and (v, u) exist in the graph, attributes for the new undirected edge will be a combination of the attributes of the directed edges. The edge data is updated in the (arbitrary) order that the edges are encountered. For more customized control of the edge attributes use add_edge().

This returns a “deepcopy” of the edge, node, and graph attributes which attempts to completely copy all of the data and references.

This is in contrast to the similar G=DiGraph(D) which returns a shallow copy of the data.

See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html.

Warning: If you have subclassed DiGraph to use dict-like objects in the data structure, those changes do not transfer to the Graph created by this method.

Examples

>>> G = nx.path_graph(2)  # or MultiGraph, etc
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1), (1, 0)]
>>> G2 = H.to_undirected()
>>> list(G2.edges)
[(0, 1)]

to_undirected_class()

Returns the class to use for empty undirected copies.

If you subclass the base classes, use this to designate what directed class to use for to_directed() copies.

property type

type attribute for every node. :rtype: dict

Type: return

update(edges=None, nodes=None)

Update the graph using nodes/edges/graphs as input.

Like dict.update, this method takes a graph as input, adding the graph’s nodes and edges to this graph. It can also take two inputs: edges and nodes. Finally it can take either edges or nodes. To specify only nodes the keyword nodes must be used.

The collections of edges and nodes are treated similarly to the add_edges_from/add_nodes_from methods. When iterated, they should yield 2-tuples (u, v) or 3-tuples (u, v, datadict).

Parameters

edges (Graph object, collection of edges, or None) – The first parameter can be a graph or some edges. If it has attributes nodes and edges, then it is taken to be a Graph-like object and those attributes are used as collections of nodes and edges to be added to the graph. If the first parameter does not have those attributes, it is treated as a collection of edges and added to the graph. If the first argument is None, no edges are added.
nodes (collection of nodes, or None) – The second parameter is treated as a collection of nodes to be added to the graph unless it is None. If edges is None and nodes is None an exception is raised. If the first parameter is a Graph, then nodes is ignored.

Examples

>>> G = nx.path_graph(5)
>>> G.update(nx.complete_graph(range(4, 10)))
>>> from itertools import combinations
>>> edges = (
...     (u, v, {"power": u * v})
...     for u, v in combinations(range(10, 20), 2)
...     if u * v < 225
... )
>>> nodes = [1000]  # for singleton, use a container
>>> G.update(edges, nodes)

Notes

It you want to update the graph using an adjacency structure it is straightforward to obtain the edges/nodes from adjacency. The following examples provide common cases, your adjacency may be slightly different and require tweaks of these examples:

>>> # dict-of-set/list/tuple
>>> adj = {1: {2, 3}, 2: {1, 3}, 3: {1, 2}}
>>> e = [(u, v) for u, nbrs in adj.items() for v in nbrs]
>>> G.update(edges=e, nodes=adj)

>>> DG = nx.DiGraph()
>>> # dict-of-dict-of-attribute
>>> adj = {1: {2: 1.3, 3: 0.7}, 2: {1: 1.4}, 3: {1: 0.7}}
>>> e = [
...     (u, v, {"weight": d})
...     for u, nbrs in adj.items()
...     for v, d in nbrs.items()
... ]
>>> DG.update(edges=e, nodes=adj)

>>> # dict-of-dict-of-dict
>>> adj = {1: {2: {"weight": 1.3}, 3: {"color": 0.7, "weight": 1.2}}}
>>> e = [
...     (u, v, {"weight": d})
...     for u, nbrs in adj.items()
...     for v, d in nbrs.items()
... ]
>>> DG.update(edges=e, nodes=adj)

>>> # predecessor adjacency (dict-of-set)
>>> pred = {1: {2, 3}, 2: {3}, 3: {3}}
>>> e = [(v, u) for u, nbrs in pred.items() for v in nbrs]

>>> # MultiGraph dict-of-dict-of-dict-of-attribute
>>> MDG = nx.MultiDiGraph()
>>> adj = {
...     1: {2: {0: {"weight": 1.3}, 1: {"weight": 1.2}}},
...     3: {2: {0: {"weight": 0.7}}},
... }
>>> e = [
...     (u, v, ekey, d)
...     for u, nbrs in adj.items()
...     for v, keydict in nbrs.items()
...     for ekey, d in keydict.items()
... ]
>>> MDG.update(edges=e)

See also

add_edges_from(): add multiple edges to a graph
add_nodes_from(): add multiple nodes to a graph

property users

list of graph users. :rtype: list

Type: return

property weight

weight attribute for every edge. :rtype: dict

Type: return