# Source code for networkx.classes.function

"""Functional interface to graph methods and assorted utilities.
"""

from collections import Counter
from itertools import chain

import networkx as nx
from networkx.utils import pairwise, not_implemented_for

from networkx.classes.graphviews import subgraph_view, reverse_view

__all__ = ['nodes', 'edges', 'degree', 'degree_histogram', 'neighbors',
'number_of_nodes', 'number_of_edges', 'density',
'is_directed', 'info', 'freeze', 'is_frozen',
'subgraph', 'subgraph_view', 'induced_subgraph', 'reverse_view',
'edge_subgraph', 'restricted_view',
'to_directed', 'to_undirected',
'create_empty_copy', 'set_node_attributes',
'get_node_attributes', 'set_edge_attributes',
'get_edge_attributes', 'all_neighbors', 'non_neighbors',
'non_edges', 'common_neighbors', 'is_weighted',
'is_negatively_weighted', 'is_empty',
'selfloop_edges', 'nodes_with_selfloops', 'number_of_selfloops',
]

[docs]def nodes(G): """Returns an iterator over the graph nodes.""" return G.nodes()
[docs]def edges(G, nbunch=None): """Returns an edge view of edges incident to nodes in nbunch. Return all edges if nbunch is unspecified or nbunch=None. For digraphs, edges=out_edges """ return G.edges(nbunch)
[docs]def degree(G, nbunch=None, weight=None): """Returns a degree view of single node or of nbunch of nodes. If nbunch is omitted, then return degrees of *all* nodes. """ return G.degree(nbunch, weight)
[docs]def neighbors(G, n): """Returns a list of nodes connected to node n. """ return G.neighbors(n)
[docs]def number_of_nodes(G): """Returns the number of nodes in the graph.""" return G.number_of_nodes()
[docs]def number_of_edges(G): """Returns the number of edges in the graph. """ return G.number_of_edges()
[docs]def density(G): r"""Returns the density of a graph. The density for undirected graphs is .. math:: d = \frac{2m}{n(n-1)}, and for directed graphs is .. math:: d = \frac{m}{n(n-1)}, where n is the number of nodes and m is the number of edges in G. Notes ----- The density is 0 for a graph without edges and 1 for a complete graph. The density of multigraphs can be higher than 1. Self loops are counted in the total number of edges so graphs with self loops can have density higher than 1. """ n = number_of_nodes(G) m = number_of_edges(G) if m == 0 or n <= 1: return 0 d = m / (n * (n - 1)) if not G.is_directed(): d *= 2 return d
[docs]def degree_histogram(G): """Returns a list of the frequency of each degree value. Parameters ---------- G : Networkx graph A graph Returns ------- hist : list A list of frequencies of degrees. The degree values are the index in the list. Notes ----- Note: the bins are width one, hence len(list) can be large (Order(number_of_edges)) """ counts = Counter(d for n, d in G.degree()) return [counts.get(i, 0) for i in range(max(counts) + 1)]
[docs]def is_directed(G): """ Return True if graph is directed.""" return G.is_directed()
def frozen(*args, **kwargs): """Dummy method for raising errors when trying to modify frozen graphs""" raise nx.NetworkXError("Frozen graph can't be modified")
[docs]def freeze(G): """Modify graph to prevent further change by adding or removing nodes or edges. Node and edge data can still be modified. Parameters ---------- G : graph A NetworkX graph Examples -------- >>> G = nx.path_graph(4) >>> G = nx.freeze(G) >>> try: ... G.add_edge(4, 5) ... except nx.NetworkXError as e: ... print(str(e)) Frozen graph can't be modified Notes ----- To "unfreeze" a graph you must make a copy by creating a new graph object: >>> graph = nx.path_graph(4) >>> frozen_graph = nx.freeze(graph) >>> unfrozen_graph = nx.Graph(frozen_graph) >>> nx.is_frozen(unfrozen_graph) False See Also -------- is_frozen """ G.add_node = frozen G.add_nodes_from = frozen G.remove_node = frozen G.remove_nodes_from = frozen G.add_edge = frozen G.add_edges_from = frozen G.add_weighted_edges_from = frozen G.remove_edge = frozen G.remove_edges_from = frozen G.clear = frozen G.frozen = True return G
[docs]def is_frozen(G): """Returns True if graph is frozen. Parameters ---------- G : graph A NetworkX graph See Also -------- freeze """ try: return G.frozen except AttributeError: return False
[docs]def add_star(G_to_add_to, nodes_for_star, **attr): """Add a star to Graph G_to_add_to. The first node in nodes_for_star is the middle of the star. It is connected to all other nodes. Parameters ---------- G_to_add_to : graph A NetworkX graph nodes_for_star : iterable container A container of nodes. attr : keyword arguments, optional (default= no attributes) Attributes to add to every edge in star. See Also -------- add_path, add_cycle Examples -------- >>> G = nx.Graph() >>> nx.add_star(G, [0, 1, 2, 3]) >>> nx.add_star(G, [10, 11, 12], weight=2) """ nlist = iter(nodes_for_star) try: v = next(nlist) except StopIteration: return G_to_add_to.add_node(v) edges = ((v, n) for n in nlist) G_to_add_to.add_edges_from(edges, **attr)
[docs]def subgraph(G, nbunch): """Returns the subgraph induced on nodes in nbunch. Parameters ---------- G : graph A NetworkX graph nbunch : list, iterable A container of nodes that will be iterated through once (thus it should be an iterator or be iterable). Each element of the container should be a valid node type: any hashable type except None. If nbunch is None, return all edges data in the graph. Nodes in nbunch that are not in the graph will be (quietly) ignored. Notes ----- subgraph(G) calls G.subgraph() """ return G.subgraph(nbunch)
[docs]def induced_subgraph(G, nbunch): """Returns a SubGraph view of G showing only nodes in nbunch. The induced subgraph of a graph on a set of nodes N is the graph with nodes N and edges from G which have both ends in N. Parameters ---------- G : NetworkX Graph nbunch : node, container of nodes or None (for all nodes) Returns ------- subgraph : SubGraph View A read-only view of the subgraph in G induced by the nodes. Changes to the graph G will be reflected in the view. Notes ----- To create a mutable subgraph with its own copies of nodes edges and attributes use subgraph.copy() or Graph(subgraph) For an inplace reduction of a graph to a subgraph you can remove nodes: G.remove_nodes_from(n in G if n not in set(nbunch)) If you are going to compute subgraphs of your subgraphs you could end up with a chain of views that can be very slow once the chain has about 15 views in it. If they are all induced subgraphs, you can short-cut the chain by making them all subgraphs of the original graph. The graph class method G.subgraph does this when G is a subgraph. In contrast, this function allows you to choose to build chains or not, as you wish. The returned subgraph is a view on G. Examples -------- >>> import networkx as nx >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> H = G.subgraph([0, 1, 2]) >>> list(H.edges) [(0, 1), (1, 2)] """ induced_nodes = nx.filters.show_nodes(G.nbunch_iter(nbunch)) return nx.graphviews.subgraph_view(G, induced_nodes)
[docs]def edge_subgraph(G, edges): """Returns a view of the subgraph induced by the specified edges. The induced subgraph contains each edge in edges and each node incident to any of those edges. Parameters ---------- G : NetworkX Graph edges : iterable An iterable of edges. Edges not present in G are ignored. Returns ------- subgraph : SubGraph View A read-only edge-induced subgraph of G. Changes to G are reflected in the view. Notes ----- To create a mutable subgraph with its own copies of nodes edges and attributes use subgraph.copy() or Graph(subgraph) If you create a subgraph of a subgraph recursively you can end up with a chain of subgraphs that becomes very slow with about 15 nested subgraph views. Luckily the edge_subgraph filter nests nicely so you can use the original graph as G in this function to avoid chains. We do not rule out chains programmatically so that odd cases like an edge_subgraph of a restricted_view can be created. Examples -------- >>> import networkx as nx >>> 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)] """ nxf = nx.filters edges = set(edges) nodes = set() for e in edges: nodes.update(e[:2]) induced_nodes = nxf.show_nodes(nodes) if G.is_multigraph(): if G.is_directed(): induced_edges = nxf.show_multidiedges(edges) else: induced_edges = nxf.show_multiedges(edges) else: if G.is_directed(): induced_edges = nxf.show_diedges(edges) else: induced_edges = nxf.show_edges(edges) return nx.graphviews.subgraph_view(G, induced_nodes, induced_edges)
[docs]def restricted_view(G, nodes, edges): """Returns a view of G with hidden nodes and edges. The resulting subgraph filters out node nodes and edges edges. Filtered out nodes also filter out any of their edges. Parameters ---------- G : NetworkX Graph nodes : iterable An iterable of nodes. Nodes not present in G are ignored. edges : iterable An iterable of edges. Edges not present in G are ignored. Returns ------- subgraph : SubGraph View A read-only restricted view of G filtering out nodes and edges. Changes to G are reflected in the view. Notes ----- To create a mutable subgraph with its own copies of nodes edges and attributes use subgraph.copy() or Graph(subgraph) If you create a subgraph of a subgraph recursively you may end up with a chain of subgraph views. Such chains can get quite slow for lengths near 15. To avoid long chains, try to make your subgraph based on the original graph. We do not rule out chains programmatically so that odd cases like an edge_subgraph of a restricted_view can be created. Examples -------- >>> import networkx as nx >>> G = nx.path_graph(5) >>> H = nx.restricted_view(G, [0], [(1, 2), (3, 4)]) >>> list(H.nodes) [1, 2, 3, 4] >>> list(H.edges) [(2, 3)] """ nxf = nx.filters hide_nodes = nxf.hide_nodes(nodes) if G.is_multigraph(): if G.is_directed(): hide_edges = nxf.hide_multidiedges(edges) else: hide_edges = nxf.hide_multiedges(edges) else: if G.is_directed(): hide_edges = nxf.hide_diedges(edges) else: hide_edges = nxf.hide_edges(edges) return nx.graphviews.subgraph_view(G, hide_nodes, hide_edges)
[docs]def to_directed(graph): """Returns a directed view of the graph graph. Identical to graph.to_directed(as_view=True) Note that graph.to_directed defaults to as_view=False while this function always provides a view. """ return graph.to_directed(as_view=True)
[docs]def to_undirected(graph): """Returns an undirected view of the graph graph. Identical to graph.to_undirected(as_view=True) Note that graph.to_undirected defaults to as_view=False while this function always provides a view. """ return graph.to_undirected(as_view=True)
[docs]def create_empty_copy(G, with_data=True): """Returns a copy of the graph G with all of the edges removed. Parameters ---------- G : graph A NetworkX graph with_data : bool (default=True) Propagate Graph and Nodes data to the new graph. See Also ----- empty_graph """ H = G.__class__() H.add_nodes_from(G.nodes(data=with_data)) if with_data: H.graph.update(G.graph) return H
[docs]def info(G, n=None): """Print short summary of information for the graph G or the node n. Parameters ---------- G : Networkx graph A graph n : node (any hashable) A node in the graph G """ info = '' # append this all to a string if n is None: info += f"Name: {G.name}\n" type_name = [type(G).__name__] info += f"Type: {','.join(type_name)}\n" info += f"Number of nodes: {G.number_of_nodes()}\n" info += f"Number of edges: {G.number_of_edges()}\n" nnodes = G.number_of_nodes() if len(G) > 0: if G.is_directed(): deg = sum(d for n, d in G.in_degree()) / float(nnodes) info += f"Average in degree: {deg:8.4f}\n" deg = sum(d for n, d in G.out_degree()) / float(nnodes) info += f"Average out degree: {deg:8.4f}" else: s = sum(dict(G.degree()).values()) info += f"Average degree: {(float(s) / float(nnodes)):8.4f}" else: if n not in G: raise nx.NetworkXError(f"node {n} not in graph") info += f"Node {n} has the following properties:\n" info += f"Degree: {G.degree(n)}\n" info += "Neighbors: " info += ' '.join(str(nbr) for nbr in G.neighbors(n)) return info
[docs]def set_node_attributes(G, values, name=None): """Sets node attributes from a given value or dictionary of values. .. Warning:: The call order of arguments values and name switched between v1.x & v2.x. Parameters ---------- G : NetworkX Graph values : scalar value, dict-like What the node attribute should be set to. If values is not a dictionary, then it is treated as a single attribute value that is then applied to every node in G. This means that if you provide a mutable object, like a list, updates to that object will be reflected in the node attribute for every node. The attribute name will be name. If values is a dict or a dict of dict, it should be keyed by node to either an attribute value or a dict of attribute key/value pairs used to update the node's attributes. name : string (optional, default=None) Name of the node attribute to set if values is a scalar. Examples -------- After computing some property of the nodes of a graph, you may want to assign a node attribute to store the value of that property for each node:: >>> G = nx.path_graph(3) >>> bb = nx.betweenness_centrality(G) >>> isinstance(bb, dict) True >>> nx.set_node_attributes(G, bb, 'betweenness') >>> G.nodes[1]['betweenness'] 1.0 If you provide a list as the second argument, updates to the list will be reflected in the node attribute for each node:: >>> G = nx.path_graph(3) >>> labels = [] >>> nx.set_node_attributes(G, labels, 'labels') >>> labels.append('foo') >>> G.nodes[0]['labels'] ['foo'] >>> G.nodes[1]['labels'] ['foo'] >>> G.nodes[2]['labels'] ['foo'] If you provide a dictionary of dictionaries as the second argument, the outer dictionary is assumed to be keyed by node to an inner dictionary of node attributes for that node:: >>> G = nx.path_graph(3) >>> attrs = {0: {'attr1': 20, 'attr2': 'nothing'}, 1: {'attr2': 3}} >>> nx.set_node_attributes(G, attrs) >>> G.nodes[0]['attr1'] 20 >>> G.nodes[0]['attr2'] 'nothing' >>> G.nodes[1]['attr2'] 3 >>> G.nodes[2] {} """ # Set node attributes based on type of values if name is not None: # values must not be a dict of dict try: # values is a dict for n, v in values.items(): try: G.nodes[n][name] = values[n] except KeyError: pass except AttributeError: # values is a constant for n in G: G.nodes[n][name] = values else: # values must be dict of dict for n, d in values.items(): try: G.nodes[n].update(d) except KeyError: pass
[docs]def get_node_attributes(G, name): """Get node attributes from graph Parameters ---------- G : NetworkX Graph name : string Attribute name Returns ------- Dictionary of attributes keyed by node. Examples -------- >>> G = nx.Graph() >>> G.add_nodes_from([1, 2, 3], color='red') >>> color = nx.get_node_attributes(G, 'color') >>> color[1] 'red' """ return {n: d[name] for n, d in G.nodes.items() if name in d}
[docs]def set_edge_attributes(G, values, name=None): """Sets edge attributes from a given value or dictionary of values. .. Warning:: The call order of arguments values and name switched between v1.x & v2.x. Parameters ---------- G : NetworkX Graph values : scalar value, dict-like What the edge attribute should be set to. If values is not a dictionary, then it is treated as a single attribute value that is then applied to every edge in G. This means that if you provide a mutable object, like a list, updates to that object will be reflected in the edge attribute for each edge. The attribute name will be name. If values is a dict or a dict of dict, it should be keyed by edge tuple to either an attribute value or a dict of attribute key/value pairs used to update the edge's attributes. For multigraphs, the edge tuples must be of the form (u, v, key), where u and v are nodes and key is the edge key. For non-multigraphs, the keys must be tuples of the form (u, v). name : string (optional, default=None) Name of the edge attribute to set if values is a scalar. Examples -------- After computing some property of the edges of a graph, you may want to assign a edge attribute to store the value of that property for each edge:: >>> G = nx.path_graph(3) >>> bb = nx.edge_betweenness_centrality(G, normalized=False) >>> nx.set_edge_attributes(G, bb, 'betweenness') >>> G.edges[1, 2]['betweenness'] 2.0 If you provide a list as the second argument, updates to the list will be reflected in the edge attribute for each edge:: >>> labels = [] >>> nx.set_edge_attributes(G, labels, 'labels') >>> labels.append('foo') >>> G.edges[0, 1]['labels'] ['foo'] >>> G.edges[1, 2]['labels'] ['foo'] If you provide a dictionary of dictionaries as the second argument, the entire dictionary will be used to update edge attributes:: >>> G = nx.path_graph(3) >>> attrs = {(0, 1): {'attr1': 20, 'attr2': 'nothing'}, ... (1, 2): {'attr2': 3}} >>> nx.set_edge_attributes(G, attrs) >>> G[0][1]['attr1'] 20 >>> G[0][1]['attr2'] 'nothing' >>> G[1][2]['attr2'] 3 """ if name is not None: # values does not contain attribute names try: # if values is a dict using .items() => {edge: value} if G.is_multigraph(): for (u, v, key), value in values.items(): try: G[u][v][key][name] = value except KeyError: pass else: for (u, v), value in values.items(): try: G[u][v][name] = value except KeyError: pass except AttributeError: # treat values as a constant for u, v, data in G.edges(data=True): data[name] = values else: # values consists of doct-of-dict {edge: {attr: value}} shape if G.is_multigraph(): for (u, v, key), d in values.items(): try: G[u][v][key].update(d) except KeyError: pass else: for (u, v), d in values.items(): try: G[u][v].update(d) except KeyError: pass
[docs]def get_edge_attributes(G, name): """Get edge attributes from graph Parameters ---------- G : NetworkX Graph name : string Attribute name Returns ------- Dictionary of attributes keyed by edge. For (di)graphs, the keys are 2-tuples of the form: (u, v). For multi(di)graphs, the keys are 3-tuples of the form: (u, v, key). Examples -------- >>> G = nx.Graph() >>> nx.add_path(G, [1, 2, 3], color='red') >>> color = nx.get_edge_attributes(G, 'color') >>> color[(1, 2)] 'red' """ if G.is_multigraph(): edges = G.edges(keys=True, data=True) else: edges = G.edges(data=True) return {x[:-1]: x[-1][name] for x in edges if name in x[-1]}
[docs]def all_neighbors(graph, node): """Returns all of the neighbors of a node in the graph. If the graph is directed returns predecessors as well as successors. Parameters ---------- graph : NetworkX graph Graph to find neighbors. node : node The node whose neighbors will be returned. Returns ------- neighbors : iterator Iterator of neighbors """ if graph.is_directed(): values = chain(graph.predecessors(node), graph.successors(node)) else: values = graph.neighbors(node) return values
[docs]def non_neighbors(graph, node): """Returns the non-neighbors of the node in the graph. Parameters ---------- graph : NetworkX graph Graph to find neighbors. node : node The node whose neighbors will be returned. Returns ------- non_neighbors : iterator Iterator of nodes in the graph that are not neighbors of the node. """ nbors = set(neighbors(graph, node)) | {node} return (nnode for nnode in graph if nnode not in nbors)
[docs]def non_edges(graph): """Returns the non-existent edges in the graph. Parameters ---------- graph : NetworkX graph. Graph to find non-existent edges. Returns ------- non_edges : iterator Iterator of edges that are not in the graph. """ if graph.is_directed(): for u in graph: for v in non_neighbors(graph, u): yield (u, v) else: nodes = set(graph) while nodes: u = nodes.pop() for v in nodes - set(graph[u]): yield (u, v)
[docs]@not_implemented_for('directed') def common_neighbors(G, u, v): """Returns the common neighbors of two nodes in a graph. Parameters ---------- G : graph A NetworkX undirected graph. u, v : nodes Nodes in the graph. Returns ------- cnbors : iterator Iterator of common neighbors of u and v in the graph. Raises ------ NetworkXError If u or v is not a node in the graph. Examples -------- >>> G = nx.complete_graph(5) >>> sorted(nx.common_neighbors(G, 0, 1)) [2, 3, 4] """ if u not in G: raise nx.NetworkXError('u is not in the graph.') if v not in G: raise nx.NetworkXError('v is not in the graph.') # Return a generator explicitly instead of yielding so that the above # checks are executed eagerly. return (w for w in G[u] if w in G[v] and w not in (u, v))
[docs]def is_weighted(G, edge=None, weight='weight'): """Returns True if G has weighted edges. Parameters ---------- G : graph A NetworkX graph. edge : tuple, optional A 2-tuple specifying the only edge in G that will be tested. If None, then every edge in G is tested. weight: string, optional The attribute name used to query for edge weights. Returns ------- bool A boolean signifying if G, or the specified edge, is weighted. Raises ------ NetworkXError If the specified edge does not exist. Examples -------- >>> G = nx.path_graph(4) >>> nx.is_weighted(G) False >>> nx.is_weighted(G, (2, 3)) False >>> G = nx.DiGraph() >>> G.add_edge(1, 2, weight=1) >>> nx.is_weighted(G) True """ if edge is not None: data = G.get_edge_data(*edge) if data is None: msg = f'Edge {edge!r} does not exist.' raise nx.NetworkXError(msg) return weight in data if is_empty(G): # Special handling required since: all([]) == True return False return all(weight in data for u, v, data in G.edges(data=True))
[docs]def is_negatively_weighted(G, edge=None, weight='weight'): """Returns True if G has negatively weighted edges. Parameters ---------- G : graph A NetworkX graph. edge : tuple, optional A 2-tuple specifying the only edge in G that will be tested. If None, then every edge in G is tested. weight: string, optional The attribute name used to query for edge weights. Returns ------- bool A boolean signifying if G, or the specified edge, is negatively weighted. Raises ------ NetworkXError If the specified edge does not exist. Examples -------- >>> G = nx.Graph() >>> G.add_edges_from([(1, 3), (2, 4), (2, 6)]) >>> G.add_edge(1, 2, weight=4) >>> nx.is_negatively_weighted(G, (1, 2)) False >>> G[2][4]['weight'] = -2 >>> nx.is_negatively_weighted(G) True >>> G = nx.DiGraph() >>> edges = [('0', '3', 3), ('0', '1', -5), ('1', '0', -2)] >>> G.add_weighted_edges_from(edges) >>> nx.is_negatively_weighted(G) True """ if edge is not None: data = G.get_edge_data(*edge) if data is None: msg = f'Edge {edge!r} does not exist.' raise nx.NetworkXError(msg) return weight in data and data[weight] < 0 return any(weight in data and data[weight] < 0 for u, v, data in G.edges(data=True))
[docs]def is_empty(G): """Returns True if G has no edges. Parameters ---------- G : graph A NetworkX graph. Returns ------- bool True if G has no edges, and False otherwise. Notes ----- An empty graph can have nodes but not edges. The empty graph with zero nodes is known as the null graph. This is an $O(n)$ operation where n is the number of nodes in the graph. """ return not any(G.adj.values())
[docs]def nodes_with_selfloops(G): """Returns an iterator over nodes with self loops. A node with a self loop has an edge with both ends adjacent to that node. Returns ------- nodelist : iterator A iterator over nodes with self loops. See Also -------- selfloop_edges, number_of_selfloops Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_edge(1, 1) >>> G.add_edge(1, 2) >>> list(nx.nodes_with_selfloops(G)) [1] """ return (n for n, nbrs in G.adj.items() if n in nbrs)