Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

Source code for networkx.classes.graph

"""Base class for undirected graphs.

The Graph class allows any hashable object as a node
and can associate key/value attribute pairs with each undirected edge.

Self-loops are allowed but multiple edges are not (see MultiGraph).

For directed graphs see DiGraph and MultiDiGraph.
"""
#    Copyright (C) 2004-2015 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
from copy import deepcopy
import networkx as nx
from networkx.exception import NetworkXError
import networkx.convert as convert

__author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
                            'Pieter Swart (swart@lanl.gov)',
                            'Dan Schult(dschult@colgate.edu)'])


[docs]class Graph(object): """ Base class for undirected graphs. A Graph stores nodes and edges with optional data, or attributes. Graphs hold undirected edges. Self loops are allowed but multiple (parallel) edges are not. Nodes can be arbitrary (hashable) Python objects with optional key/value attributes. Edges are represented as links between nodes with optional key/value attributes. Parameters ---------- data : input graph Data to initialize graph. If data=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 NumPy matrix or 2d ndarray, 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 -------- DiGraph MultiGraph MultiDiGraph Examples -------- Create an empty graph structure (a "null graph") with no nodes and no edges. >>> G = nx.Graph() G can be grown in several ways. **Nodes:** Add one node at a time: >>> G.add_node(1) Add the nodes from any container (a list, dict, set or even the lines from a file or the nodes from another graph). >>> G.add_nodes_from([2,3]) >>> G.add_nodes_from(range(100,110)) >>> H=nx.Graph() >>> H.add_path([0,1,2,3,4,5,6,7,8,9]) >>> G.add_nodes_from(H) In addition to strings and integers any hashable Python object (except None) can represent a node, e.g. a customized node object, or even another Graph. >>> G.add_node(H) **Edges:** G can also be grown by adding edges. Add one edge, >>> G.add_edge(1, 2) a list of edges, >>> G.add_edges_from([(1,2),(1,3)]) or a collection of edges, >>> G.add_edges_from(H.edges()) If some edges connect nodes not yet in the graph, the nodes are added automatically. There are no errors when adding nodes or edges that already exist. **Attributes:** Each graph, node, and edge can hold key/value attribute pairs in an associated attribute dictionary (the keys must be hashable). By default these are empty, but can be added or changed using add_edge, add_node or direct manipulation of the attribute dictionaries named graph, node and edge respectively. >>> G = nx.Graph(day="Friday") >>> G.graph {'day': 'Friday'} Add node attributes using add_node(), add_nodes_from() or G.node >>> G.add_node(1, time='5pm') >>> G.add_nodes_from([3], time='2pm') >>> G.node[1] {'time': '5pm'} >>> G.node[1]['room'] = 714 >>> del G.node[1]['room'] # remove attribute >>> G.nodes(data=True) [(1, {'time': '5pm'}), (3, {'time': '2pm'})] Warning: adding a node to G.node does not add it to the graph. Add edge attributes using add_edge(), add_edges_from(), subscript notation, or G.edge. >>> G.add_edge(1, 2, weight=4.7 ) >>> G.add_edges_from([(3,4),(4,5)], color='red') >>> G.add_edges_from([(1,2,{'color':'blue'}), (2,3,{'weight':8})]) >>> G[1][2]['weight'] = 4.7 >>> G.edge[1][2]['weight'] = 4 **Shortcuts:** Many common graph features allow python syntax to speed reporting. >>> 1 in G # check if node in graph True >>> [n for n in G if n<3] # iterate through nodes [1, 2] >>> len(G) # number of nodes in graph 5 The fastest way to traverse all edges of a graph is via adjacency_iter(), but the edges() method is often more convenient. >>> for n,nbrsdict in G.adjacency_iter(): ... for nbr,eattr in nbrsdict.items(): ... if 'weight' in eattr: ... (n,nbr,eattr['weight']) (1, 2, 4) (2, 1, 4) (2, 3, 8) (3, 2, 8) >>> G.edges(data='weight') [(1, 2, 4), (2, 3, 8), (3, 4, None), (4, 5, None)] **Reporting:** Simple graph information is obtained using methods. Iterator versions of many reporting methods exist for efficiency. Methods exist for reporting nodes(), edges(), neighbors() and degree() as well as the number of nodes and edges. For details on these and other miscellaneous methods, see below. **Subclasses (Advanced):** The Graph class uses a dict-of-dict-of-dict data structure. The outer dict (node_dict) holds adjacency lists keyed by node. The next dict (adjlist) represents the adjacency list and holds edge data keyed by neighbor. The inner dict (edge_attr) represents the edge data and holds edge attribute values keyed by attribute names. Each of these three dicts can be replaced by a user defined dict-like object. In general, the dict-like features should be maintained but extra features can be added. To replace one of the dicts create a new graph class by changing the class(!) variable holding the factory for that dict-like structure. The variable names are node_dict_factory, adjlist_dict_factory and edge_attr_dict_factory. node_dict_factory : function, (default: dict) Factory function to be used to create the outer-most dict in the data structure that holds adjacency lists keyed by node. It should require no arguments and return a dict-like object. adjlist_dict_factory : function, (default: dict) Factory function to be used to create the adjacency list dict which holds edge data keyed by neighbor. It should require no arguments and return a dict-like object edge_attr_dict_factory : function, (default: dict) Factory function to be used to create the edge attribute dict which holds attrbute values keyed by attribute name. It should require no arguments and return a dict-like object. Examples -------- Create a graph object that tracks the order nodes are added. >>> from collections import OrderedDict >>> class OrderedNodeGraph(nx.Graph): ... node_dict_factory=OrderedDict >>> G=OrderedNodeGraph() >>> G.add_nodes_from( (2,1) ) >>> G.nodes() [2, 1] >>> G.add_edges_from( ((2,2), (2,1), (1,1)) ) >>> G.edges() [(2, 1), (2, 2), (1, 1)] Create a graph object that tracks the order nodes are added and for each node track the order that neighbors are added. >>> class OrderedGraph(nx.Graph): ... node_dict_factory = OrderedDict ... adjlist_dict_factory = OrderedDict >>> G = OrderedGraph() >>> G.add_nodes_from( (2,1) ) >>> G.nodes() [2, 1] >>> G.add_edges_from( ((2,2), (2,1), (1,1)) ) >>> G.edges() [(2, 2), (2, 1), (1, 1)] Create a low memory graph class that effectively disallows edge attributes by using a single attribute dict for all edges. This reduces the memory used, but you lose edge attributes. >>> class ThinGraph(nx.Graph): ... all_edge_dict = {'weight': 1} ... def single_edge_dict(self): ... return self.all_edge_dict ... edge_attr_dict_factory = single_edge_dict >>> G = ThinGraph() >>> G.add_edge(2,1) >>> G.edges(data= True) [(1, 2, {'weight': 1})] >>> G.add_edge(2,2) >>> G[2][1] is G[2][2] True """ node_dict_factory = dict adjlist_dict_factory = dict edge_attr_dict_factory = dict
[docs] def __init__(self, data=None, **attr): """Initialize a graph with edges, name, graph attributes. Parameters ---------- data : input graph Data to initialize graph. If data=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 NumPy matrix or 2d ndarray, a SciPy sparse matrix, or a PyGraphviz graph. name : string, optional (default='') An optional name for the 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'} """ self.node_dict_factory = ndf = self.node_dict_factory self.adjlist_dict_factory = self.adjlist_dict_factory self.edge_attr_dict_factory = self.edge_attr_dict_factory self.graph = {} # dictionary for graph attributes self.node = ndf() # empty node attribute dict self.adj = ndf() # empty adjacency dict # attempt to load graph with data if data is not None: convert.to_networkx_graph(data, create_using=self) # load graph attributes (must be after convert) self.graph.update(attr) self.edge = self.adj
@property def name(self): return self.graph.get('name', '') @name.setter def name(self, s): self.graph['name'] = s def __str__(self): """Return the graph name. Returns ------- name : string The name of the graph. Examples -------- >>> G = nx.Graph(name='foo') >>> str(G) 'foo' """ return self.name
[docs] def __iter__(self): """Iterate over the nodes. Use the expression 'for n in G'. Returns ------- niter : iterator An iterator over all nodes in the graph. Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) """ return iter(self.node)
[docs] def __contains__(self, n): """Return True if n is a node, False otherwise. Use the expression 'n in G'. Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> 1 in G True """ try: return n in self.node except TypeError: return False
[docs] def __len__(self): """Return the number of nodes. Use the expression 'len(G)'. Returns ------- nnodes : int The number of nodes in the graph. Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> len(G) 4 """ return len(self.node)
[docs] def __getitem__(self, n): """Return a dict of neighbors of node n. Use the expression 'G[n]'. Parameters ---------- n : node A node in the graph. Returns ------- adj_dict : dictionary The adjacency dictionary for nodes connected to n. Notes ----- G[n] is similar to G.neighbors(n) but the internal data dictionary is returned instead of a list. Assigning G[n] will corrupt the internal graph data structure. Use G[n] for reading data only. Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> G[0] {1: {}} """ return self.adj[n]
[docs] def add_node(self, n, attr_dict=None, **attr): """Add a single node n and update node attributes. Parameters ---------- n : node A node can be any hashable Python object except None. attr_dict : dictionary, optional (default= no attributes) Dictionary of node attributes. Key/value pairs will update existing data associated with the node. attr : keyword arguments, optional Set or change 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. """ # set up attribute dict if attr_dict is None: attr_dict = attr else: try: attr_dict.update(attr) except AttributeError: raise NetworkXError( "The attr_dict argument must be a dictionary.") if n not in self.node: self.adj[n] = self.adjlist_dict_factory() self.node[n] = attr_dict else: # update attr even if node already exists self.node[n].update(attr_dict)
[docs] def add_nodes_from(self, nodes, **attr): """Add multiple nodes. Parameters ---------- nodes : 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 generally. 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.node[1]['size'] 11 >>> H = nx.Graph() >>> H.add_nodes_from(G.nodes(data=True)) >>> H.node[1]['size'] 11 """ for n in nodes: # keep all this inside try/except because # CPython throws TypeError on n not in self.succ, # while pre-2.7.5 ironpython throws on self.succ[n] try: if n not in self.node: self.adj[n] = self.adjlist_dict_factory() self.node[n] = attr.copy() else: self.node[n].update(attr) except TypeError: nn, ndict = n if nn not in self.node: self.adj[nn] = self.adjlist_dict_factory() newdict = attr.copy() newdict.update(ndict) self.node[nn] = newdict else: olddict = self.node[nn] olddict.update(attr) olddict.update(ndict)
[docs] def remove_node(self, 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.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2]) >>> G.edges() [(0, 1), (1, 2)] >>> G.remove_node(1) >>> G.edges() [] """ adj = self.adj try: nbrs = list(adj[n].keys()) # keys handles self-loops (allow mutation later) del self.node[n] except KeyError: # NetworkXError if n not in self raise NetworkXError("The node %s is not in the graph." % (n,)) for u in nbrs: del adj[u][n] # remove all edges n-u in graph del adj[n] # now remove node
[docs] def remove_nodes_from(self, 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.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2]) >>> e = G.nodes() >>> e [0, 1, 2] >>> G.remove_nodes_from(e) >>> G.nodes() [] """ adj = self.adj for n in nodes: try: del self.node[n] for u in list(adj[n].keys()): # keys() handles self-loops del adj[u][n] # (allows mutation of dict in loop) del adj[n] except KeyError: pass
[docs] def nodes_iter(self, data=False): """Return an iterator over the nodes. Parameters ---------- data : boolean, optional (default=False) If False the iterator returns nodes. If True return a two-tuple of node and node data dictionary Returns ------- niter : iterator An iterator over nodes. If data=True the iterator gives two-tuples containing (node, node data, dictionary) Notes ----- If the node data is not required it is simpler and equivalent to use the expression 'for n in G'. >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2]) Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2]) >>> [d for n,d in G.nodes_iter(data=True)] [{}, {}, {}] """ if data: return iter(self.node.items()) return iter(self.node)
[docs] def nodes(self, data=False): """Return a list of the nodes in the graph. Parameters ---------- data : boolean, optional (default=False) If False return a list of nodes. If True return a two-tuple of node and node data dictionary Returns ------- nlist : list A list of nodes. If data=True a list of two-tuples containing (node, node data dictionary). Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2]) >>> G.nodes() [0, 1, 2] >>> G.add_node(1, time='5pm') >>> G.nodes(data=True) [(0, {}), (1, {'time': '5pm'}), (2, {})] """ return list(self.nodes_iter(data=data))
[docs] def number_of_nodes(self): """Return the number of nodes in the graph. Returns ------- nnodes : int The number of nodes in the graph. See Also -------- order, __len__ which are identical Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2]) >>> len(G) 3 """ return len(self.node)
[docs] def order(self): """Return the number of nodes in the graph. Returns ------- nnodes : int The number of nodes in the graph. See Also -------- number_of_nodes, __len__ which are identical """ return len(self.node)
[docs] def has_node(self, n): """Return True if the graph contains the node n. Parameters ---------- n : node Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2]) >>> G.has_node(0) True It is more readable and simpler to use >>> 0 in G True """ try: return n in self.node except TypeError: return False
[docs] def add_edge(self, u, v, attr_dict=None, **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 providing a dictionary with key/value pairs. See examples below. Parameters ---------- u,v : nodes Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects. attr_dict : dictionary, optional (default= no attributes) Dictionary of edge attributes. Key/value pairs will update existing data associated with the edge. 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 as the edge weight a numerical value assigned to a keyword which by default is 'weight'. 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) """ # set up attribute dictionary if attr_dict is None: attr_dict = attr else: try: attr_dict.update(attr) except AttributeError: raise NetworkXError( "The attr_dict argument must be a dictionary.") # add nodes if u not in self.node: self.adj[u] = self.adjlist_dict_factory() self.node[u] = {} if v not in self.node: self.adj[v] = self.adjlist_dict_factory() self.node[v] = {} # add the edge datadict = self.adj[u].get(v, self.edge_attr_dict_factory()) datadict.update(attr_dict) self.adj[u][v] = datadict self.adj[v][u] = datadict
[docs] def add_edges_from(self, ebunch, attr_dict=None, **attr): """Add all the edges in ebunch. Parameters ---------- ebunch : container of edges Each edge given in the container will be added to the graph. The edges must be given as as 2-tuples (u,v) or 3-tuples (u,v,d) where d is a dictionary containing edge data. attr_dict : dictionary, optional (default= no attributes) Dictionary of edge attributes. Key/value pairs will update existing data associated with each edge. 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 edges take precedence over attributes specified generally. 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') """ # set up attribute dict if attr_dict is None: attr_dict = attr else: try: attr_dict.update(attr) except AttributeError: raise NetworkXError( "The attr_dict argument must be a dictionary.") # process ebunch for e in ebunch: ne = len(e) if ne == 3: u, v, dd = e elif ne == 2: u, v = e dd = {} # doesnt need edge_attr_dict_factory else: raise NetworkXError( "Edge tuple %s must be a 2-tuple or 3-tuple." % (e,)) if u not in self.node: self.adj[u] = self.adjlist_dict_factory() self.node[u] = {} if v not in self.node: self.adj[v] = self.adjlist_dict_factory() self.node[v] = {} datadict = self.adj[u].get(v, self.edge_attr_dict_factory()) datadict.update(attr_dict) datadict.update(dd) self.adj[u][v] = datadict self.adj[v][u] = datadict
[docs] def add_weighted_edges_from(self, ebunch, weight='weight', **attr): """Add all the edges in ebunch as weighted edges with specified weights. Parameters ---------- ebunch : 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)]) """ self.add_edges_from(((u, v, {weight: d}) for u, v, d in ebunch), **attr)
[docs] def remove_edge(self, u, v): """Remove the edge between u and v. Parameters ---------- u,v: nodes 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 >>> G.add_path([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 """ try: del self.adj[u][v] if u != v: # self-loop needs only one entry removed del self.adj[v][u] except KeyError: raise NetworkXError("The edge %s-%s is not in the graph" % (u, v))
[docs] def remove_edges_from(self, 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.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> ebunch=[(1,2),(2,3)] >>> G.remove_edges_from(ebunch) """ adj = self.adj for e in ebunch: u, v = e[:2] # ignore edge data if present if u in adj and v in adj[u]: del adj[u][v] if u != v: # self loop needs only one entry removed del adj[v][u]
[docs] def has_edge(self, u, v): """Return True if the edge (u,v) is in the graph. Parameters ---------- u,v : nodes Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects. Returns ------- edge_ind : bool True if edge is in the graph, False otherwise. Examples -------- Can be called either using two nodes u,v or edge tuple (u,v) >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> 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 all equivalent: >>> G.has_edge(0,1) True >>> 1 in G[0] # though this gives KeyError if 0 not in G True """ try: return v in self.adj[u] except KeyError: return False
[docs] def neighbors(self, n): """Return a list of the nodes connected to the node n. Parameters ---------- n : node A node in the graph Returns ------- nlist : list A list of nodes that are adjacent to n. Raises ------ NetworkXError If the node n is not in the graph. Notes ----- It is usually more convenient (and faster) to access the adjacency dictionary as G[n]: >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_edge('a','b',weight=7) >>> G['a'] {'b': {'weight': 7}} Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> G.neighbors(0) [1] """ try: return list(self.adj[n]) except KeyError: raise NetworkXError("The node %s is not in the graph." % (n,))
[docs] def neighbors_iter(self, n): """Return an iterator over all neighbors of node n. Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> [n for n in G.neighbors_iter(0)] [1] Notes ----- It is faster to use the idiom "in G[0]", e.g. >>> G = nx.path_graph(4) >>> [n for n in G[0]] [1] """ try: return iter(self.adj[n]) except KeyError: raise NetworkXError("The node %s is not in the graph." % (n,))
[docs] def edges(self, nbunch=None, data=False, default=None): """Return a list of edges. Edges are returned as tuples with optional data in the order (node, neighbor, data). Parameters ---------- nbunch : iterable container, optional (default= all nodes) A container of nodes. The container will be iterated through once. data : bool, optional (default=False) Return two tuples (u,v) (False) or three-tuples (u,v,data) (True). Returns -------- edge_list: list of edge tuples Edges that are adjacent to any node in nbunch, or a list of all edges if nbunch is not specified. See Also -------- edges_iter : return an iterator over the 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.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2]) >>> G.add_edge(2,3,weight=5) >>> G.edges() [(0, 1), (1, 2), (2, 3)] >>> G.edges(data=True) # default edge data is {} (empty dictionary) [(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})] >>> list(G.edges_iter(data='weight', default=1)) [(0, 1, 1), (1, 2, 1), (2, 3, 5)] >>> G.edges([0,3]) [(0, 1), (3, 2)] >>> G.edges(0) [(0, 1)] """ return list(self.edges_iter(nbunch, data, default))
[docs] def edges_iter(self, nbunch=None, data=False, default=None): """Return an iterator over the edges. Edges are returned as tuples with optional data in the order (node, neighbor, data). Parameters ---------- nbunch : iterable container, optional (default= all nodes) A container of nodes. The container will be iterated through once. 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 dont have the requested attribute. Only relevant if data is not True or False. Returns ------- edge_iter : iterator An iterator of (u,v) or (u,v,d) tuples of edges. See Also -------- edges : return a list of 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.Graph() # or MultiGraph, etc >>> G.add_path([0,1,2]) >>> G.add_edge(2,3,weight=5) >>> [e for e in G.edges_iter()] [(0, 1), (1, 2), (2, 3)] >>> list(G.edges_iter(data=True)) # default data is {} (empty dict) [(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})] >>> list(G.edges_iter(data='weight', default=1)) [(0, 1, 1), (1, 2, 1), (2, 3, 5)] >>> list(G.edges_iter([0,3])) [(0, 1), (3, 2)] >>> list(G.edges_iter(0)) [(0, 1)] """ seen = {} # helper dict to keep track of multiply stored edges if nbunch is None: nodes_nbrs = self.adj.items() else: nodes_nbrs = ((n, self.adj[n]) for n in self.nbunch_iter(nbunch)) if data is True: for n, nbrs in nodes_nbrs: for nbr, ddict in nbrs.items(): if nbr not in seen: yield (n, nbr, ddict) seen[n] = 1 elif data is not False: for n, nbrs in nodes_nbrs: for nbr, ddict in nbrs.items(): if nbr not in seen: d = ddict[data] if data in ddict else default yield (n, nbr, d) seen[n] = 1 else: # data is False for n, nbrs in nodes_nbrs: for nbr in nbrs: if nbr not in seen: yield (n, nbr) seen[n] = 1 del seen
[docs] def get_edge_data(self, u, v, default=None): """Return the attribute dictionary associated with edge (u,v). Parameters ---------- u,v : nodes default: any Python object (default=None) Value to return if the edge (u,v) is not found. Returns ------- edge_dict : dictionary The edge attribute dictionary. Notes ----- It is faster to use G[u][v]. >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> G[0][1] {} Warning: Assigning G[u][v] corrupts the graph data structure. But it is safe to assign attributes to that dictionary, >>> G[0][1]['weight'] = 7 >>> G[0][1]['weight'] 7 >>> G[1][0]['weight'] 7 Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> 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 """ try: return self.adj[u][v] except KeyError: return default
[docs] def adjacency_list(self): """Return an adjacency list representation of the graph. The output adjacency list is in the order of G.nodes(). For directed graphs, only outgoing adjacencies are included. Returns ------- adj_list : lists of lists The adjacency structure of the graph as a list of lists. See Also -------- adjacency_iter Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> G.adjacency_list() # in order given by G.nodes() [[1], [0, 2], [1, 3], [2]] """ return list(map(list, iter(self.adj.values())))
[docs] def adjacency_iter(self): """Return an iterator of (node, adjacency dict) tuples for all nodes. This is the fastest way to look at every edge. For directed graphs, only outgoing adjacencies are included. Returns ------- adj_iter : iterator An iterator of (node, adjacency dictionary) for all nodes in the graph. See Also -------- adjacency_list Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> [(n,nbrdict) for n,nbrdict in G.adjacency_iter()] [(0, {1: {}}), (1, {0: {}, 2: {}}), (2, {1: {}, 3: {}}), (3, {2: {}})] """ return iter(self.adj.items())
[docs] def degree(self, nbunch=None, weight=None): """Return the degree of a node or nodes. The node degree is the number of edges adjacent to that node. Parameters ---------- nbunch : iterable container, optional (default=all nodes) A container of nodes. The container will be iterated through once. 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. The degree is the sum of the edge weights adjacent to the node. Returns ------- nd : dictionary, or number A dictionary with nodes as keys and degree as values or a number if a single node is specified. Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> G.degree(0) 1 >>> G.degree([0,1]) {0: 1, 1: 2} >>> list(G.degree([0,1]).values()) [1, 2] """ if nbunch in self: # return a single node return next(self.degree_iter(nbunch, weight))[1] else: # return a dict return dict(self.degree_iter(nbunch, weight))
[docs] def degree_iter(self, nbunch=None, weight=None): """Return an iterator for (node, degree). The node degree is the number of edges adjacent to the node. Parameters ---------- nbunch : iterable container, optional (default=all nodes) A container of nodes. The container will be iterated through once. 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. The degree is the sum of the edge weights adjacent to the node. Returns ------- nd_iter : an iterator The iterator returns two-tuples of (node, degree). See Also -------- degree Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> list(G.degree_iter(0)) # node 0 with degree 1 [(0, 1)] >>> list(G.degree_iter([0,1])) [(0, 1), (1, 2)] """ if nbunch is None: nodes_nbrs = self.adj.items() else: nodes_nbrs = ((n, self.adj[n]) for n in self.nbunch_iter(nbunch)) if weight is None: for n, nbrs in nodes_nbrs: yield (n, len(nbrs) + (n in nbrs)) # return tuple (n,degree) else: # edge weighted graph - degree is sum of nbr edge weights for n, nbrs in nodes_nbrs: yield (n, sum((nbrs[nbr].get(weight, 1) for nbr in nbrs)) + (n in nbrs and nbrs[n].get(weight, 1)))
[docs] def clear(self): """Remove all nodes and edges from the graph. This also removes the name, and all graph, node, and edge attributes. Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> G.clear() >>> G.nodes() [] >>> G.edges() [] """ self.name = '' self.adj.clear() self.node.clear() self.graph.clear()
[docs] def copy(self): """Return a copy of the graph. Returns ------- G : Graph A copy of the graph. See Also -------- to_directed: return a directed copy of the graph. Notes ----- This makes a complete copy of the graph including all of the node or edge attributes. Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> H = G.copy() """ return deepcopy(self)
def is_multigraph(self): """Return True if graph is a multigraph, False otherwise.""" return False def is_directed(self): """Return True if graph is directed, False otherwise.""" return False
[docs] def to_directed(self): """Return a directed representation of the graph. Returns ------- G : DiGraph 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). 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, http://docs.python.org/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_path([0,1]) >>> H = G.to_directed() >>> H.edges() [(0, 1), (1, 0)] If already directed, return a (deep) copy >>> G = nx.DiGraph() # or MultiDiGraph, etc >>> G.add_path([0,1]) >>> H = G.to_directed() >>> H.edges() [(0, 1)] """ from networkx import DiGraph G = DiGraph() G.name = self.name G.add_nodes_from(self) G.add_edges_from(((u, v, deepcopy(data)) for u, nbrs in self.adjacency_iter() for v, data in nbrs.items())) G.graph = deepcopy(self.graph) G.node = deepcopy(self.node) return G
[docs] def to_undirected(self): """Return an undirected copy of the graph. Returns ------- G : Graph/MultiGraph A deepcopy of the graph. See Also -------- copy, add_edge, add_edges_from 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 G=DiGraph(D) which returns a shallow copy of the data. See the Python copy module for more information on shallow and deep copies, http://docs.python.org/library/copy.html. Examples -------- >>> G = nx.Graph() # or MultiGraph, etc >>> G.add_path([0,1]) >>> H = G.to_directed() >>> H.edges() [(0, 1), (1, 0)] >>> G2 = H.to_undirected() >>> G2.edges() [(0, 1)] """ return deepcopy(self)
[docs] def subgraph(self, nbunch): """Return the subgraph induced on nodes in nbunch. The induced subgraph of the graph contains the nodes in nbunch and the edges between those nodes. Parameters ---------- nbunch : list, iterable A container of nodes which will be iterated through once. Returns ------- G : Graph A subgraph of the graph with the same edge attributes. Notes ----- The graph, edge or node attributes just point to the original graph. So changes to the node or edge structure will not be reflected in the original graph while changes to the attributes will. To create a subgraph with its own copy of the edge/node attributes use: nx.Graph(G.subgraph(nbunch)) If edge attributes are containers, a deep copy can be obtained using: G.subgraph(nbunch).copy() 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)]) Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> H = G.subgraph([0,1,2]) >>> H.edges() [(0, 1), (1, 2)] """ bunch = self.nbunch_iter(nbunch) # create new graph and copy subgraph into it H = self.__class__() # copy node and attribute dictionaries for n in bunch: H.node[n] = self.node[n] # namespace shortcuts for speed H_adj = H.adj self_adj = self.adj # add nodes and edges (undirected method) for n in H.node: Hnbrs = H.adjlist_dict_factory() H_adj[n] = Hnbrs for nbr, d in self_adj[n].items(): if nbr in H_adj: # add both representations of edge: n-nbr and nbr-n Hnbrs[nbr] = d H_adj[nbr][n] = d H.graph = self.graph return H
[docs] def nodes_with_selfloops(self): """Return a list of nodes with self loops. A node with a self loop has an edge with both ends adjacent to that node. Returns ------- nodelist : list A list of 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) >>> G.nodes_with_selfloops() [1] """ return [n for n, nbrs in self.adj.items() if n in nbrs]
[docs] def selfloop_edges(self, data=False, default=None): """Return a list of selfloop edges. A selfloop edge has the same node at both ends. Parameters ---------- data : string or bool, optional (default=False) Return selfloop edges as two tuples (u,v) (data=False) or three-tuples (u,v,datadict) (data=True) or three-tuples (u,v,datavalue) (data='attrname') default : value, optional (default=None) Value used for edges that dont have the requested attribute. Only relevant if data is not True or False. Returns ------- edgelist : list of edge tuples A list of all selfloop edges. See Also -------- nodes_with_selfloops, number_of_selfloops Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_edge(1,1) >>> G.add_edge(1,2) >>> G.selfloop_edges() [(1, 1)] >>> G.selfloop_edges(data=True) [(1, 1, {})] """ if data is True: return [(n, n, nbrs[n]) for n, nbrs in self.adj.items() if n in nbrs] elif data is not False: return [(n, n, nbrs[n].get(data, default)) for n, nbrs in self.adj.items() if n in nbrs] else: return [(n, n) for n, nbrs in self.adj.items() if n in nbrs]
[docs] def number_of_selfloops(self): """Return the number of selfloop edges. A selfloop edge has the same node at both ends. Returns ------- nloops : int The number of selfloops. See Also -------- nodes_with_selfloops, selfloop_edges Examples -------- >>> G=nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_edge(1,1) >>> G.add_edge(1,2) >>> G.number_of_selfloops() 1 """ return len(self.selfloop_edges())
[docs] def size(self, weight=None): """Return the number of edges. 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 ------- nedges : int The number of edges or sum of edge weights in the graph. See Also -------- number_of_edges Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> 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 """ s = sum(self.degree(weight=weight).values()) / 2 if weight is None: return int(s) else: return float(s)
[docs] def number_of_edges(self, u=None, v=None): """Return the number of edges between two nodes. Parameters ---------- u,v : nodes, optional (default=all edges) 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 : int The number of edges in the graph. If nodes u and v are specified return the number of edges between those nodes. See Also -------- size Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> G.number_of_edges() 3 >>> G.number_of_edges(0,1) 1 >>> e = (0,1) >>> G.number_of_edges(*e) 1 """ if u is None: return int(self.size()) if v in self.adj[u]: return 1 else: return 0
[docs] def add_star(self, nodes, **attr): """Add a star. The first node in nodes is the middle of the star. It is connected to all other nodes. Parameters ---------- nodes : 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() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_star([0,1,2,3]) >>> G.add_star([10,11,12],weight=2) """ nlist = list(nodes) v = nlist[0] edges = ((v, n) for n in nlist[1:]) self.add_edges_from(edges, **attr)
[docs] def add_path(self, nodes, **attr): """Add a path. Parameters ---------- nodes : iterable container A container of nodes. A path will be constructed from the nodes (in order) and added to the graph. attr : keyword arguments, optional (default= no attributes) Attributes to add to every edge in path. See Also -------- add_star, add_cycle Examples -------- >>> G=nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> G.add_path([10,11,12],weight=7) """ nlist = list(nodes) edges = zip(nlist[:-1], nlist[1:]) self.add_edges_from(edges, **attr)
[docs] def add_cycle(self, nodes, **attr): """Add a cycle. Parameters ---------- nodes: iterable container A container of nodes. A cycle will be constructed from the nodes (in order) and added to the graph. attr : keyword arguments, optional (default= no attributes) Attributes to add to every edge in cycle. See Also -------- add_path, add_star Examples -------- >>> G=nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_cycle([0,1,2,3]) >>> G.add_cycle([10,11,12],weight=7) """ nlist = list(nodes) edges = zip(nlist, nlist[1:] + [nlist[0]]) self.add_edges_from(edges, **attr)
[docs] def nbunch_iter(self, nbunch=None): """Return an iterator of 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 : iterable container, optional (default=all nodes) A container of nodes. The container will be iterated through once. Returns ------- niter : iterator An iterator over nodes in nbunch that are also in the graph. If nbunch is None, iterate over all nodes in the graph. Raises ------ NetworkXError If nbunch is not a node or 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. """ if nbunch is None: # include all nodes via iterator bunch = iter(self.adj.keys()) elif nbunch in self: # if nbunch is a single node bunch = iter([nbunch]) else: # if nbunch is a sequence of nodes def bunch_iter(nlist, adj): try: for n in nlist: if n in adj: yield n except TypeError as e: message = e.args[0] # capture error for non-sequence/iterator nbunch. if 'iter' in message: raise NetworkXError( "nbunch is not a node or a sequence of nodes.") # capture error for unhashable node. elif 'hashable' in message: raise NetworkXError( "Node %s in the sequence nbunch is not a valid node."%n) else: raise bunch = bunch_iter(nbunch, self.adj) return bunch