Source code for networkx.generators.random_graphs

# -*- coding: utf-8 -*-
"""
Generators for random graphs.

"""
#    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.
__author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)',
                        'Pieter Swart (swart@lanl.gov)',
                        'Dan Schult (dschult@colgate.edu)'])
import itertools
import random
import math
import networkx as nx
from networkx.generators.classic import empty_graph, path_graph, complete_graph

from collections import defaultdict

__all__ = ['fast_gnp_random_graph',
           'gnp_random_graph',
           'dense_gnm_random_graph',
           'gnm_random_graph',
           'erdos_renyi_graph',
           'binomial_graph',
           'newman_watts_strogatz_graph',
           'watts_strogatz_graph',
           'connected_watts_strogatz_graph',
           'random_regular_graph',
           'barabasi_albert_graph',
           'powerlaw_cluster_graph',
           'duplication_divergence_graph',
           'random_lobster',
           'random_shell_graph',
           'random_powerlaw_tree',
           'random_powerlaw_tree_sequence']


#-------------------------------------------------------------------------
#  Some Famous Random Graphs
#-------------------------------------------------------------------------


[docs]def fast_gnp_random_graph(n, p, seed=None, directed=False): """Returns a `G_{n,p}` random graph, also known as an Erdős-Rényi graph or a binomial graph. Parameters ---------- n : int The number of nodes. p : float Probability for edge creation. seed : int, optional Seed for random number generator (default=None). directed : bool, optional (default=False) If ``True``, this function returns a directed graph. Notes ----- The `G_{n,p}` graph algorithm chooses each of the `[n (n - 1)] / 2` (undirected) or `n (n - 1)` (directed) possible edges with probability `p`. This algorithm runs in `O(n + m)` time, where `m` is the expected number of edges, which equals `p n (n - 1) / 2`. This should be faster than :func:`gnp_random_graph` when `p` is small and the expected number of edges is small (that is, the graph is sparse). See Also -------- gnp_random_graph References ---------- .. [1] Vladimir Batagelj and Ulrik Brandes, "Efficient generation of large random networks", Phys. Rev. E, 71, 036113, 2005. """ G = empty_graph(n) G.name="fast_gnp_random_graph(%s,%s)"%(n,p) if not seed is None: random.seed(seed) if p <= 0 or p >= 1: return nx.gnp_random_graph(n,p,directed=directed) w = -1 lp = math.log(1.0 - p) if directed: G = nx.DiGraph(G) # Nodes in graph are from 0,n-1 (start with v as the first node index). v = 0 while v < n: lr = math.log(1.0 - random.random()) w = w + 1 + int(lr/lp) if v == w: # avoid self loops w = w + 1 while w >= n and v < n: w = w - n v = v + 1 if v == w: # avoid self loops w = w + 1 if v < n: G.add_edge(v, w) else: # Nodes in graph are from 0,n-1 (start with v as the second node index). v = 1 while v < n: lr = math.log(1.0 - random.random()) w = w + 1 + int(lr/lp) while w >= v and v < n: w = w - v v = v + 1 if v < n: G.add_edge(v, w) return G
[docs]def gnp_random_graph(n, p, seed=None, directed=False): """Returns a `G_{n,p}` random graph, also known as an Erdős-Rényi graph or a binomial graph. The `G_{n,p}` model chooses each of the possible edges with probability ``p``. The functions :func:`binomial_graph` and :func:`erdos_renyi_graph` are aliases of this function. Parameters ---------- n : int The number of nodes. p : float Probability for edge creation. seed : int, optional Seed for random number generator (default=None). directed : bool, optional (default=False) If ``True``, this function returns a directed graph. See Also -------- fast_gnp_random_graph Notes ----- This algorithm runs in `O(n^2)` time. For sparse graphs (that is, for small values of `p`), :func:`fast_gnp_random_graph` is a faster algorithm. References ---------- .. [1] P. Erdős and A. Rényi, On Random Graphs, Publ. Math. 6, 290 (1959). .. [2] E. N. Gilbert, Random Graphs, Ann. Math. Stat., 30, 1141 (1959). """ if directed: G=nx.DiGraph() else: G=nx.Graph() G.add_nodes_from(range(n)) G.name="gnp_random_graph(%s,%s)"%(n,p) if p<=0: return G if p>=1: return complete_graph(n,create_using=G) if not seed is None: random.seed(seed) if G.is_directed(): edges=itertools.permutations(range(n),2) else: edges=itertools.combinations(range(n),2) for e in edges: if random.random() < p: G.add_edge(*e) return G # add some aliases to common names
binomial_graph=gnp_random_graph erdos_renyi_graph=gnp_random_graph
[docs]def dense_gnm_random_graph(n, m, seed=None): """Returns a `G_{n,m}` random graph. In the `G_{n,m}` model, a graph is chosen uniformly at random from the set of all graphs with `n` nodes and `m` edges. This algorithm should be faster than :func:`gnm_random_graph` for dense graphs. Parameters ---------- n : int The number of nodes. m : int The number of edges. seed : int, optional Seed for random number generator (default=None). See Also -------- gnm_random_graph() Notes ----- Algorithm by Keith M. Briggs Mar 31, 2006. Inspired by Knuth's Algorithm S (Selection sampling technique), in section 3.4.2 of [1]_. References ---------- .. [1] Donald E. Knuth, The Art of Computer Programming, Volume 2/Seminumerical algorithms, Third Edition, Addison-Wesley, 1997. """ mmax=n*(n-1)/2 if m>=mmax: G=complete_graph(n) else: G=empty_graph(n) G.name="dense_gnm_random_graph(%s,%s)"%(n,m) if n==1 or m>=mmax: return G if seed is not None: random.seed(seed) u=0 v=1 t=0 k=0 while True: if random.randrange(mmax-t)<m-k: G.add_edge(u,v) k+=1 if k==m: return G t+=1 v+=1 if v==n: # go to next row of adjacency matrix u+=1 v=u+1
[docs]def gnm_random_graph(n, m, seed=None, directed=False): """Returns a `G_{n,m}` random graph. In the `G_{n,m}` model, a graph is chosen uniformly at random from the set of all graphs with `n` nodes and `m` edges. This algorithm should be faster than :func:`dense_gnm_random_graph` for sparse graphs. Parameters ---------- n : int The number of nodes. m : int The number of edges. seed : int, optional Seed for random number generator (default=None). directed : bool, optional (default=False) If True return a directed graph See also -------- dense_gnm_random_graph """ if directed: G=nx.DiGraph() else: G=nx.Graph() G.add_nodes_from(range(n)) G.name="gnm_random_graph(%s,%s)"%(n,m) if seed is not None: random.seed(seed) if n==1: return G max_edges=n*(n-1) if not directed: max_edges/=2.0 if m>=max_edges: return complete_graph(n,create_using=G) nlist=G.nodes() edge_count=0 while edge_count < m: # generate random edge,u,v u = random.choice(nlist) v = random.choice(nlist) if u==v or G.has_edge(u,v): continue else: G.add_edge(u,v) edge_count=edge_count+1 return G
[docs]def newman_watts_strogatz_graph(n, k, p, seed=None): """Return a Newman–Watts–Strogatz small-world graph. Parameters ---------- n : int The number of nodes. k : int Each node is joined with its ``k`` nearest neighbors in a ring topology. p : float The probability of adding a new edge for each edge. seed : int, optional The seed for the random number generator (the default is ``None``). Notes ----- First create a ring over ``n`` nodes. Then each node in the ring is connected with its ``k`` nearest neighbors (or ``k - 1`` neighbors if ``k`` is odd). Then shortcuts are created by adding new edges as follows: for each edge ``(u, v)`` in the underlying "``n``-ring with ``k`` nearest neighbors" with probability ``p`` add a new edge ``(u, w)`` with randomly-chosen existing node ``w``. In contrast with :func:`watts_strogatz_graph`, no edges are removed. See Also -------- watts_strogatz_graph() References ---------- .. [1] M. E. J. Newman and D. J. Watts, Renormalization group analysis of the small-world network model, Physics Letters A, 263, 341, 1999. http://dx.doi.org/10.1016/S0375-9601(99)00757-4 """ if seed is not None: random.seed(seed) if k>=n: raise nx.NetworkXError("k>=n, choose smaller k or larger n") G=empty_graph(n) G.name="newman_watts_strogatz_graph(%s,%s,%s)"%(n,k,p) nlist = G.nodes() fromv = nlist # connect the k/2 neighbors for j in range(1, k // 2+1): tov = fromv[j:] + fromv[0:j] # the first j are now last for i in range(len(fromv)): G.add_edge(fromv[i], tov[i]) # for each edge u-v, with probability p, randomly select existing # node w and add new edge u-w e = G.edges() for (u, v) in e: if random.random() < p: w = random.choice(nlist) # no self-loops and reject if edge u-w exists # is that the correct NWS model? while w == u or G.has_edge(u, w): w = random.choice(nlist) if G.degree(u) >= n-1: break # skip this rewiring else: G.add_edge(u,w) return G
[docs]def watts_strogatz_graph(n, k, p, seed=None): """Return a Watts–Strogatz small-world graph. Parameters ---------- n : int The number of nodes k : int Each node is joined with its ``k`` nearest neighbors in a ring topology. p : float The probability of rewiring each edge seed : int, optional Seed for random number generator (default=None) See Also -------- newman_watts_strogatz_graph() connected_watts_strogatz_graph() Notes ----- First create a ring over ``n`` nodes. Then each node in the ring is joined to its ``k`` nearest neighbors (or ``k - 1`` neighbors if ``k`` is odd). Then shortcuts are created by replacing some edges as follows: for each edge ``(u, v)`` in the underlying "``n``-ring with ``k`` nearest neighbors" with probability ``p`` replace it with a new edge ``(u, w)`` with uniformly random choice of existing node ``w``. In contrast with :func:`newman_watts_strogatz_graph`, the random rewiring does not increase the number of edges. The rewired graph is not guaranteed to be connected as in :func:`connected_watts_strogatz_graph`. References ---------- .. [1] Duncan J. Watts and Steven H. Strogatz, Collective dynamics of small-world networks, Nature, 393, pp. 440--442, 1998. """ if k>=n: raise nx.NetworkXError("k>=n, choose smaller k or larger n") if seed is not None: random.seed(seed) G = nx.Graph() G.name="watts_strogatz_graph(%s,%s,%s)"%(n,k,p) nodes = list(range(n)) # nodes are labeled 0 to n-1 # connect each node to k/2 neighbors for j in range(1, k // 2+1): targets = nodes[j:] + nodes[0:j] # first j nodes are now last in list G.add_edges_from(zip(nodes,targets)) # rewire edges from each node # loop over all nodes in order (label) and neighbors in order (distance) # no self loops or multiple edges allowed for j in range(1, k // 2+1): # outer loop is neighbors targets = nodes[j:] + nodes[0:j] # first j nodes are now last in list # inner loop in node order for u,v in zip(nodes,targets): if random.random() < p: w = random.choice(nodes) # Enforce no self-loops or multiple edges while w == u or G.has_edge(u, w): w = random.choice(nodes) if G.degree(u) >= n-1: break # skip this rewiring else: G.remove_edge(u,v) G.add_edge(u,w) return G
[docs]def connected_watts_strogatz_graph(n, k, p, tries=100, seed=None): """Returns a connected Watts–Strogatz small-world graph. Attempts to generate a connected graph by repeated generation of Watts–Strogatz small-world graphs. An exception is raised if the maximum number of tries is exceeded. Parameters ---------- n : int The number of nodes k : int Each node is joined with its ``k`` nearest neighbors in a ring topology. p : float The probability of rewiring each edge tries : int Number of attempts to generate a connected graph. seed : int, optional The seed for random number generator. See Also -------- newman_watts_strogatz_graph() watts_strogatz_graph() """ G = watts_strogatz_graph(n, k, p, seed) t=1 while not nx.is_connected(G): G = watts_strogatz_graph(n, k, p, seed) t=t+1 if t>tries: raise nx.NetworkXError("Maximum number of tries exceeded") return G
[docs]def random_regular_graph(d, n, seed=None): """Returns a random ``d``-regular graph on ``n`` nodes. The resulting graph has no self-loops or parallel edges. Parameters ---------- d : int The degree of each node. n : integer The number of nodes. The value of ``n * d`` must be even. seed : hashable object The seed for random number generator. Notes ----- The nodes are numbered from ``0`` to ``n - 1``. Kim and Vu's paper [2]_ shows that this algorithm samples in an asymptotically uniform way from the space of random graphs when `d = O(n^{1 / 3 - \epsilon})`. Raises ------ NetworkXError If ``n * d`` is odd or ``d`` is greater than or equal to ``n``. References ---------- .. [1] A. Steger and N. Wormald, Generating random regular graphs quickly, Probability and Computing 8 (1999), 377-396, 1999. http://citeseer.ist.psu.edu/steger99generating.html .. [2] Jeong Han Kim and Van H. Vu, Generating random regular graphs, Proceedings of the thirty-fifth ACM symposium on Theory of computing, San Diego, CA, USA, pp 213--222, 2003. http://portal.acm.org/citation.cfm?id=780542.780576 """ if (n * d) % 2 != 0: raise nx.NetworkXError("n * d must be even") if not 0 <= d < n: raise nx.NetworkXError("the 0 <= d < n inequality must be satisfied") if d == 0: return empty_graph(n) if seed is not None: random.seed(seed) def _suitable(edges, potential_edges): # Helper subroutine to check if there are suitable edges remaining # If False, the generation of the graph has failed if not potential_edges: return True for s1 in potential_edges: for s2 in potential_edges: # Two iterators on the same dictionary are guaranteed # to visit it in the same order if there are no # intervening modifications. if s1 == s2: # Only need to consider s1-s2 pair one time break if s1 > s2: s1, s2 = s2, s1 if (s1, s2) not in edges: return True return False def _try_creation(): # Attempt to create an edge set edges = set() stubs = list(range(n)) * d while stubs: potential_edges = defaultdict(lambda: 0) random.shuffle(stubs) stubiter = iter(stubs) for s1, s2 in zip(stubiter, stubiter): if s1 > s2: s1, s2 = s2, s1 if s1 != s2 and ((s1, s2) not in edges): edges.add((s1, s2)) else: potential_edges[s1] += 1 potential_edges[s2] += 1 if not _suitable(edges, potential_edges): return None # failed to find suitable edge set stubs = [node for node, potential in potential_edges.items() for _ in range(potential)] return edges # Even though a suitable edge set exists, # the generation of such a set is not guaranteed. # Try repeatedly to find one. edges = _try_creation() while edges is None: edges = _try_creation() G = nx.Graph() G.name = "random_regular_graph(%s, %s)" % (d, n) G.add_edges_from(edges) return G
def _random_subset(seq,m): """ Return m unique elements from seq. This differs from random.sample which can return repeated elements if seq holds repeated elements. """ targets=set() while len(targets)<m: x=random.choice(seq) targets.add(x) return targets
[docs]def barabasi_albert_graph(n, m, seed=None): """Returns a random graph according to the Barabási–Albert preferential attachment model. A graph of ``n`` nodes is grown by attaching new nodes each with ``m`` edges that are preferentially attached to existing nodes with high degree. Parameters ---------- n : int Number of nodes m : int Number of edges to attach from a new node to existing nodes seed : int, optional Seed for random number generator (default=None). Returns ------- G : Graph Raises ------ NetworkXError If ``m`` does not satisfy ``1 <= m < n``. References ---------- .. [1] A. L. Barabási and R. Albert "Emergence of scaling in random networks", Science 286, pp 509-512, 1999. """ if m < 1 or m >=n: raise nx.NetworkXError("Barabási–Albert network must have m >= 1" " and m < n, m = %d, n = %d" % (m, n)) if seed is not None: random.seed(seed) # Add m initial nodes (m0 in barabasi-speak) G=empty_graph(m) G.name="barabasi_albert_graph(%s,%s)"%(n,m) # Target nodes for new edges targets=list(range(m)) # List of existing nodes, with nodes repeated once for each adjacent edge repeated_nodes=[] # Start adding the other n-m nodes. The first node is m. source=m while source<n: # Add edges to m nodes from the source. G.add_edges_from(zip([source]*m,targets)) # Add one node to the list for each new edge just created. repeated_nodes.extend(targets) # And the new node "source" has m edges to add to the list. repeated_nodes.extend([source]*m) # Now choose m unique nodes from the existing nodes # Pick uniformly from repeated_nodes (preferential attachement) targets = _random_subset(repeated_nodes,m) source += 1 return G
[docs]def powerlaw_cluster_graph(n, m, p, seed=None): """Holme and Kim algorithm for growing graphs with powerlaw degree distribution and approximate average clustering. Parameters ---------- n : int the number of nodes m : int the number of random edges to add for each new node p : float, Probability of adding a triangle after adding a random edge seed : int, optional Seed for random number generator (default=None). Notes ----- The average clustering has a hard time getting above a certain cutoff that depends on ``m``. This cutoff is often quite low. The transitivity (fraction of triangles to possible triangles) seems to decrease with network size. It is essentially the Barabási–Albert (BA) growth model with an extra step that each random edge is followed by a chance of making an edge to one of its neighbors too (and thus a triangle). This algorithm improves on BA in the sense that it enables a higher average clustering to be attained if desired. It seems possible to have a disconnected graph with this algorithm since the initial ``m`` nodes may not be all linked to a new node on the first iteration like the BA model. Raises ------ NetworkXError If ``m`` does not satisfy ``1 <= m <= n`` or ``p`` does not satisfy ``0 <= p <= 1``. References ---------- .. [1] P. Holme and B. J. Kim, "Growing scale-free networks with tunable clustering", Phys. Rev. E, 65, 026107, 2002. """ if m < 1 or n < m: raise nx.NetworkXError(\ "NetworkXError must have m>1 and m<n, m=%d,n=%d"%(m,n)) if p > 1 or p < 0: raise nx.NetworkXError(\ "NetworkXError p must be in [0,1], p=%f"%(p)) if seed is not None: random.seed(seed) G=empty_graph(m) # add m initial nodes (m0 in barabasi-speak) G.name="Powerlaw-Cluster Graph" repeated_nodes=G.nodes() # list of existing nodes to sample from # with nodes repeated once for each adjacent edge source=m # next node is m while source<n: # Now add the other n-1 nodes possible_targets = _random_subset(repeated_nodes,m) # do one preferential attachment for new node target=possible_targets.pop() G.add_edge(source,target) repeated_nodes.append(target) # add one node to list for each new link count=1 while count<m: # add m-1 more new links if random.random()<p: # clustering step: add triangle neighborhood=[nbr for nbr in G.neighbors(target) \ if not G.has_edge(source,nbr) \ and not nbr==source] if neighborhood: # if there is a neighbor without a link nbr=random.choice(neighborhood) G.add_edge(source,nbr) # add triangle repeated_nodes.append(nbr) count=count+1 continue # go to top of while loop # else do preferential attachment step if above fails target=possible_targets.pop() G.add_edge(source,target) repeated_nodes.append(target) count=count+1 repeated_nodes.extend([source]*m) # add source node to list m times source += 1 return G
[docs]def duplication_divergence_graph(n, p, seed=None): """Returns an undirected graph using the duplication-divergence model. A graph of ``n`` nodes is created by duplicating the initial nodes and retaining edges incident to the original nodes with a retention probability ``p``. Parameters ---------- n : int The desired number of nodes in the graph. p : float The probability for retaining the edge of the replicated node. seed : int, optional A seed for the random number generator of ``random`` (default=None). Returns ------- G : Graph Raises ------ NetworkXError If `p` is not a valid probability. If `n` is less than 2. References ---------- .. [1] I. Ispolatov, P. L. Krapivsky, A. Yuryev, "Duplication-divergence model of protein interaction network", Phys. Rev. E, 71, 061911, 2005. """ if p > 1 or p < 0: msg = "NetworkXError p={0} is not in [0,1].".format(p) raise nx.NetworkXError(msg) if n < 2: msg = 'n must be greater than or equal to 2' raise nx.NetworkXError(msg) if seed is not None: random.seed(seed) G = nx.Graph() G.graph['name'] = "Duplication-Divergence Graph" # Initialize the graph with two connected nodes. G.add_edge(0,1) i = 2 while i < n: # Choose a random node from current graph to duplicate. random_node = random.choice(G.nodes()) # Make the replica. G.add_node(i) # flag indicates whether at least one edge is connected on the replica. flag=False for nbr in G.neighbors(random_node): if random.random() < p: # Link retention step. G.add_edge(i, nbr) flag = True if not flag: # Delete replica if no edges retained. G.remove_node(i) else: # Successful duplication. i += 1 return G
[docs]def random_lobster(n, p1, p2, seed=None): """Returns a random lobster graph. A lobster is a tree that reduces to a caterpillar when pruning all leaf nodes. A caterpillar is a tree that reduces to a path graph when pruning all leaf nodes; setting ``p2`` to zero produces a caterillar. Parameters ---------- n : int The expected number of nodes in the backbone p1 : float Probability of adding an edge to the backbone p2 : float Probability of adding an edge one level beyond backbone seed : int, optional Seed for random number generator (default=None). """ # a necessary ingredient in any self-respecting graph library if seed is not None: random.seed(seed) llen=int(2*random.random()*n + 0.5) L=path_graph(llen) L.name="random_lobster(%d,%s,%s)"%(n,p1,p2) # build caterpillar: add edges to path graph with probability p1 current_node=llen-1 for n in range(llen): if random.random()<p1: # add fuzzy caterpillar parts current_node+=1 L.add_edge(n,current_node) if random.random()<p2: # add crunchy lobster bits current_node+=1 L.add_edge(current_node-1,current_node) return L # voila, un lobster!
[docs]def random_shell_graph(constructor, seed=None): """Returns a random shell graph for the constructor given. Parameters ---------- constructor : list of three-tuples Represents the parameters for a shell, starting at the center shell. Each element of the list must be of the form ``(n, m, d)``, where ``n`` is the number of nodes in the shell, ``m`` is the number of edges in the shell, and ``d`` is the ratio of inter-shell (next) edges to intra-shell edges. If ``d`` is zero, there will be no intra-shell edges, and if ``d`` is one there will be all possible intra-shell edges. seed : int, optional Seed for random number generator (default=None). Examples -------- >>> constructor = [(10, 20, 0.8), (20, 40, 0.8)] >>> G = nx.random_shell_graph(constructor) """ G=empty_graph(0) G.name="random_shell_graph(constructor)" if seed is not None: random.seed(seed) glist=[] intra_edges=[] nnodes=0 # create gnm graphs for each shell for (n,m,d) in constructor: inter_edges=int(m*d) intra_edges.append(m-inter_edges) g=nx.convert_node_labels_to_integers( gnm_random_graph(n,inter_edges), first_label=nnodes) glist.append(g) nnodes+=n G=nx.operators.union(G,g) # connect the shells randomly for gi in range(len(glist)-1): nlist1=glist[gi].nodes() nlist2=glist[gi+1].nodes() total_edges=intra_edges[gi] edge_count=0 while edge_count < total_edges: u = random.choice(nlist1) v = random.choice(nlist2) if u==v or G.has_edge(u,v): continue else: G.add_edge(u,v) edge_count=edge_count+1 return G
[docs]def random_powerlaw_tree(n, gamma=3, seed=None, tries=100): """Returns a tree with a power law degree distribution. Parameters ---------- n : int The number of nodes. gamma : float Exponent of the power law. seed : int, optional Seed for random number generator (default=None). tries : int Number of attempts to adjust the sequence to make it a tree. Raises ------ NetworkXError If no valid sequence is found within the maximum number of attempts. Notes ----- A trial power law degree sequence is chosen and then elements are swapped with new elements from a powerlaw distribution until the sequence makes a tree (by checking, for example, that the number of edges is one smaller than the number of nodes). """ from networkx.generators.degree_seq import degree_sequence_tree try: s=random_powerlaw_tree_sequence(n, gamma=gamma, seed=seed, tries=tries) except: raise nx.NetworkXError(\ "Exceeded max (%d) attempts for a valid tree sequence."%tries) G=degree_sequence_tree(s) G.name="random_powerlaw_tree(%s,%s)"%(n,gamma) return G
[docs]def random_powerlaw_tree_sequence(n, gamma=3, seed=None, tries=100): """Returns a degree sequence for a tree with a power law distribution. Parameters ---------- n : int, The number of nodes. gamma : float Exponent of the power law. seed : int, optional Seed for random number generator (default=None). tries : int Number of attempts to adjust the sequence to make it a tree. Raises ------ NetworkXError If no valid sequence is found within the maximum number of attempts. Notes ----- A trial power law degree sequence is chosen and then elements are swapped with new elements from a power law distribution until the sequence makes a tree (by checking, for example, that the number of edges is one smaller than the number of nodes). """ if seed is not None: random.seed(seed) # get trial sequence z=nx.utils.powerlaw_sequence(n,exponent=gamma) # round to integer values in the range [0,n] zseq=[min(n, max( int(round(s)),0 )) for s in z] # another sequence to swap values from z=nx.utils.powerlaw_sequence(tries,exponent=gamma) # round to integer values in the range [0,n] swap=[min(n, max( int(round(s)),0 )) for s in z] for deg in swap: if n-sum(zseq)/2.0 == 1.0: # is a tree, return sequence return zseq index=random.randint(0,n-1) zseq[index]=swap.pop() raise nx.NetworkXError(\ "Exceeded max (%d) attempts for a valid tree sequence."%tries) return False