hKSrSSKrSSKJr SS/rS Sjr\R"SS9S S j5r\R"SS9S S j5r g)zAFunctions for computing reaching centrality of a node or a graph.N)pairwiseglobal_reaching_centralitylocal_reaching_centralityc^^[U5S- nUS::agTcSU- $[UU4Sj[U555nXC- $)aReturns the average weight of an edge in a weighted path. Parameters ---------- G : graph A networkx graph. path: list A list of vertices that define the path. weight : None or string, optional (default=None) If None, edge weights are ignored. Then the average weight of an edge is assumed to be the multiplicative inverse of the length of the path. Otherwise holds the name of the edge attribute used as weight. rc3N># UHupTRX4Tv M g7fN)edges).0ijGweights Y/var/www/html/env/lib/python3.13/site-packages/networkx/algorithms/centrality/reaching.py "_average_weight..s"Hqwwqt}V,s"%)lensumr)rpathr path_length total_weights` ` r_average_weightr sI d)a-Ka ~;H$HHL  %%r) edge_attrsc ^^ ^ [R"UTS9(a[R"S5eURTS9m T S::a[R"S5eTbU U4Sjn[R"XS9nO[R"U5n[ nUR 5VVs/sHupgU"XUTUS9PM nnn[U5m [U 4SjU55[U5S- - $s snnf) uReturns the global reaching centrality of a directed graph. The *global reaching centrality* of a weighted directed graph is the average over all nodes of the difference between the local reaching centrality of the node and the greatest local reaching centrality of any node in the graph [1]_. For more information on the local reaching centrality, see :func:`local_reaching_centrality`. Informally, the local reaching centrality is the proportion of the graph that is reachable from the neighbors of the node. Parameters ---------- G : DiGraph A networkx DiGraph. weight : None or string, optional (default=None) Attribute to use for edge weights. If ``None``, each edge weight is assumed to be one. A higher weight implies a stronger connection between nodes and a *shorter* path length. normalized : bool, optional (default=True) Whether to normalize the edge weights by the total sum of edge weights. Returns ------- h : float The global reaching centrality of the graph. Examples -------- >>> G = nx.DiGraph() >>> G.add_edge(1, 2) >>> G.add_edge(1, 3) >>> nx.global_reaching_centrality(G) 1.0 >>> G.add_edge(3, 2) >>> nx.global_reaching_centrality(G) 0.75 See also -------- local_reaching_centrality References ---------- .. [1] Mones, Enys, Lilla Vicsek, and Tamás Vicsek. "Hierarchy Measure for Complex Networks." *PLoS ONE* 7.3 (2012): e33799. https://doi.org/10.1371/journal.pone.0033799 redge weights must be positiverSize of G must be positivec.>TURTS5- $Nrgetuvdrrs r as_distance/global_reaching_centrality..as_distancegs!%%"22 2r)pathsr normalizedc3.># UH nTU- v M g7fr )r cmax_lrcs rr-global_reaching_centrality..vs(Cqw{Csr) nxis_negatively_weighted NetworkXErrorsize shortest_pathritemsmaxrr) rrr*r'shortest_paths centralitynoder)lrcr.rs ` @@rrr"sj   62>??666(Lq;<< 3))!@))!,*J*//1 1KD 1%:N1  #hG (C( (CFQJ 77  s-C4c^^^ TRTS9=m S:a%[T5S:Xa[R"S5eUc[R"TTS9(a[R"S5eT S::a[R"S5eTbU U4Sjn[R "TXS9nO[R "TUS 9nTc2TR 5(a[U5S- [T5S- - $U(a$Tb!TRTS9TR5- nOSnUU4S jUR55n[U5U- nU[T5S- - $) u%Returns the local reaching centrality of a node in a directed graph. The *local reaching centrality* of a node in a directed graph is the proportion of other nodes reachable from that node [1]_. Parameters ---------- G : DiGraph A NetworkX DiGraph. v : node A node in the directed graph `G`. paths : dictionary (default=None) If this is not `None` it must be a dictionary representation of single-source shortest paths, as computed by, for example, :func:`networkx.shortest_path` with source node `v`. Use this keyword argument if you intend to invoke this function many times but don't want the paths to be recomputed each time. weight : None or string, optional (default=None) Attribute to use for edge weights. If `None`, each edge weight is assumed to be one. A higher weight implies a stronger connection between nodes and a *shorter* path length. normalized : bool, optional (default=True) Whether to normalize the edge weights by the total sum of edge weights. Returns ------- h : float The local reaching centrality of the node ``v`` in the graph ``G``. Examples -------- >>> G = nx.DiGraph() >>> G.add_edges_from([(1, 2), (1, 3)]) >>> nx.local_reaching_centrality(G, 3) 0.0 >>> G.add_edge(3, 2) >>> nx.local_reaching_centrality(G, 3) 0.5 See also -------- global_reaching_centrality References ---------- .. [1] Mones, Enys, Lilla Vicsek, and Tamás Vicsek. "Hierarchy Measure for Complex Networks." *PLoS ONE* 7.3 (2012): e33799. https://doi.org/10.1371/journal.pone.0033799 rrrzJlocal_reaching_centrality of a single node with self-loop not well-definedrrc.>TURTS5- $r r!r#s rr'.local_reaching_centrality..as_distances#aeeFA&666r)sourcer)r>c3:># UHn[TUTS9v M g7f)rN)r)r rrrs rr,local_reaching_centrality..s OOAtF 3s) r3rr0r2r1r4 is_directedvaluesr) rr%r)rr*r'normavgwsum_avg_weightrs ` ` @rrrys7xf-- 2s1v{ X   } $ $Qv 6""#BC C 1 ""#?@ @   7$$QqEE$$Qq1E~!--//E Q3q6A:..f(vvVv$qvvx/ O  ODY%N SVaZ ((rr )NT)NNT) __doc__networkxr0networkx.utilsr__all__r _dispatchablerrr,rrrKsaG# ')D E&2X&S8'S8lX&W)'W)r