+ jRt^RIt^RIHtHtRR.t]PR4t]!R4]P!RR7]!R 4RRR R/R l444t R#) z(Function for computing walks in a graph.N)not_implemented_forpy_random_statenumber_of_walks random_walkc^RIpV^8d\RV 24h\P!VRR7pVPP P W14P4p\V4UUUUu/uF;wrVT\V4UUu/uFwrxWWW3,P4bK uppbK= p ppppV #uuppiuuppppi)a7Returns the number of walks connecting each pair of nodes in `G` A *walk* is a sequence of nodes in which each adjacent pair of nodes in the sequence is adjacent in the graph. A walk can repeat the same edge and go in the opposite direction just as people can walk on a set of paths, but standing still is not counted as part of the walk. This function only counts the walks with `walk_length` edges. Note that the number of nodes in the walk sequence is one more than `walk_length`. The number of walks can grow very quickly on a larger graph and with a larger walk length. Parameters ---------- G : NetworkX graph walk_length : int A nonnegative integer representing the length of a walk. Returns ------- dict A dictionary of dictionaries in which outer keys are source nodes, inner keys are target nodes, and inner values are the number of walks of length `walk_length` connecting those nodes. Raises ------ ValueError If `walk_length` is negative Examples -------- >>> G = nx.Graph([(0, 1), (1, 2)]) >>> walks = nx.number_of_walks(G, 2) >>> walks {0: {0: 1, 1: 0, 2: 1}, 1: {0: 0, 1: 2, 2: 0}, 2: {0: 1, 1: 0, 2: 1}} >>> total_walks = sum(sum(tgts.values()) for _, tgts in walks.items()) You can also get the number of walks from a specific source node using the returned dictionary. For example, number of walks of length 1 from node 0 can be found as follows: >>> walks = nx.number_of_walks(G, 1) >>> walks[0] {0: 0, 1: 1, 2: 0} >>> sum(walks[0].values()) # walks from 0 of length 1 1 Similarly, a target node can also be specified: >>> walks[0][1] 1 Nz"`walk_length` cannot be negative: )weight) scipy ValueErrornxadjacency_matrixsparselinalg matrix_powertocsr enumerateitem) G walk_lengthspApoweru_idxuv_idxvresults && Z/home/luca/screen-checking/.venv/lib/python3.14/site-packages/networkx/algorithms/walks.pyrr stQ=k]KLL Ad+A II   ) )! 9 ? ? AE"! $HE )A, G,heAU\"'') ), GG$  M Hs5C #B=.C =C multigraphr) edge_attrsseedc#."W9d\P!V4hTpVxVPV,;p'dVfVP\ V44pMVP 4Uu.uFqfP V^4NK pp\;QJdRV4F 'gK RM RM !RV44'd \R4h\V4^8XdR#VP\ V4V^R7^,pVxKR#uupi5i)aLYields nodes visited by a random walk starting at `start`. The generator yields nodes in walk order, including `start` as the first yielded node, and terminates when there is no valid outgoing transition. If `weight` is None, transitions are uniform over neighbors. If `weight` is a string, transitions are proportional to that edge attribute, defaulting to 1 if missing. Parameters ---------- G : NetworkX graph The input graph. start : node Starting node for the random walk. weight : string or None, optional (default=None) Edge attribute name to interpret as the transition weight. If None, each edge has weight 1. seed : integer, random_state, or None (default=None) Indicator of random number generation state. See :ref:`Randomness`. Yields ------ node The next node in the random walk Raises ------ nx.NodeNotFound If `start` is not in `G` ValueError If `weight` is not None and a negative weight is encountered. Examples -------- The `random_walk` generator is designed to be very flexible, thus there is no default condition for terminating a walk. .. warning:: Calling ``list(nx.random_walk(G, start=n))`` will result in an infinite loop if `G` is undirected (or strongly connected if directed). >>> G = nx.cycle_graph(10) To generate a walk with a given length: >>> walk_length = 4 >>> rw = nx.random_walk(G, start=0, seed=99) >>> [next(rw) for _ in range(walk_length)] [0, 9, 0, 1] or with `itertools.islice`: >>> import itertools >>> rw = nx.random_walk(G, start=0, seed=99) >>> list(itertools.islice(rw, walk_length)) [0, 9, 0, 1] One may want to terminate a walk when a specific node (or set of nodes) is reached; for example, transitioning from one "barbell" to the other: >>> G = nx.barbell_graph(5, 0) >>> terminal_nodes = set(range(5, 10)) >>> rwg = nx.random_walk(G, start=0, seed=999999) >>> list(itertools.takewhile(lambda n: n not in terminal_nodes, rwg)) [0, 2, 1, 2, 4] Or perform a walk with a termination probability for each step: >>> import random >>> random.seed(5040) >>> termination_probability = 0.25 >>> G = nx.complete_graph(10) >>> list( ... itertools.takewhile( ... lambda _: random.random() > termination_probability, ... nx.random_walk(G, start=0, seed=999), ... ) ... ) [0, 2, 9, 7] `random_walk` can be combined with distance constraints to sample local regions in a graph: >>> G = nx.balanced_tree(2, 3) >>> distance = nx.single_source_shortest_path_length(G, source=0) >>> distance_limit = 3 >>> list( ... itertools.takewhile( ... lambda n: distance[n] < distance_limit, ... nx.random_walk(G, start=0, seed=99), ... ) ... ) [0, 2, 5, 2, 6, 2, 0, 1, 0, 1, 3] The `weight` keyword can be used to indicate an edge attribute to use for weighted sampling: >>> G = nx.path_graph(3) >>> nx.set_edge_attributes(G, {(0, 1): 2, (1, 2): 10}, name="weight") >>> rw = nx.random_walk(G, start=1, weight="weight", seed=2048) >>> list(itertools.islice(rw, 10)) [1, 2, 1, 2, 1, 2, 1, 2, 1, 0] When performing a weighted walk, edges with 0 weight are ignored: >>> G = nx.star_graph(5) >>> nx.set_edge_attributes(G, {(0, n): 0 for n in range(2, len(G))}, name="weight") >>> rw = nx.random_walk(G, start=0, weight="weight") >>> list(itertools.islice(rw, 4)) [0, 1, 0, 1] For directed graphs, if a node with 0 outdegree is reached, the walk will terminate: >>> G = nx.path_graph(5, create_using=nx.DiGraph) >>> list(nx.random_walk(G, start=3)) [3, 4] Self-loop edges are included in the neighbor sampling: >>> G = nx.Graph([(0, 0)]) >>> list(itertools.islice(nx.random_walk(G, start=0), 5)) [0, 0, 0, 0, 0] Nc3*"TF q^8xK R#5i)N).0ws& r random_walk..s&#Qq5#sTFz,random_walk doesn't support negative weights)weightsk) r NodeNotFound_adjchoicelistvaluesgetanyr sumchoices)rstartrrnodenbrsnbrwtss&$$$ rrrQsJ ~ooe$$ D J&&, $  >;;tDz*D15?#7761%C?s&#&sss&#&&& !OPP3x1}<<T C1<=a@D  @s$=D1D1D D,DAD) __doc__networkxr networkx.utilsrr__all__ _dispatchablerrr#rr>s.? m ,DDN\"X&RDRtR'#Rr=