btjdZddlmZddlZddgZejddd Zdd ZeZ ejdd Z dd Z dS)zLoad centrality.) itemgetterNload_centralityedge_load_centralityweight) edge_attrsTc|[d}|D]&}t|||d|}|||vr||ndz }'|r-|}|dkr|S|d|dz |dz zz z}ni|d}|D]0}t|||d|}|D]} || xx|| z cc<1|r?|}|dkr|Sd|dz |dz zz } |D]}||xx| zcc<|S)uCompute load centrality for nodes. The load centrality of a node is the fraction of all shortest paths that pass through that node. Parameters ---------- G : graph A networkx graph. normalized : bool, optional (default=True) If True the betweenness values are normalized by b=b/(n-1)(n-2) where n is the number of nodes in G. weight : None or string, optional (default=None) If None, edge weights are ignored. Otherwise holds the name of the edge attribute used as weight. The weight of an edge is treated as the length or distance between the two sides. cutoff : bool, optional (default=None) If specified, only consider paths of length <= cutoff. Returns ------- nodes : dictionary Dictionary of nodes with centrality as the value. See Also -------- betweenness_centrality Notes ----- Load centrality is slightly different than betweenness. It was originally introduced by [2]_. For this load algorithm see [1]_. References ---------- .. [1] Mark E. J. Newman: Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. Physical Review E 64, 016132, 2001. http://journals.aps.org/pre/abstract/10.1103/PhysRevE.64.016132 .. [2] Kwang-Il Goh, Byungnam Kahng and Doochul Kim Universal behavior of Load Distribution in Scale-Free Networks. Physical Review Letters 87(27):1–4, 2001. https://doi.org/10.1103/PhysRevLett.87.278701 NFr?)_node_betweennessorderfromkeys) Gvcutoff normalizedr betweennesssourceubetweenrvkscales a/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/networkx/algorithms/centrality/load.pynewman_betweenness_centralityr s_d }  ? ?F(FFE6JJH !x--8A;;Q >KK  =GGIIEzz"" 3519";< z%_node_betweenness..ls 8 8 8IT1q$i 8 8 8rc$g|] \}}|dk |S)rr )r!r#r"s rr$z%_node_betweenness..ns!777)1dQrr r r )nx predecessor!dijkstra_predecessor_and_distanceitemssortrpoplen)rrrrrpredlengthonodesbetweenr num_pathsxr#rs rr r Vs ~6&dSSSvv=aQWXXv9 8 8 8 8F KKMMM77v777F111Ikk&#&&G 5 JJLL 99DG I!W 5 5;;E gaj944  5 a $ LL q55!a%AE*+E $ $ e# Nrci}|D]\}}d|||f<d|||f<|D]>}t|||}|D]\}}||xx|z cc<?|S)aCompute edge load. WARNING: This concept of edge load has not been analysed or discussed outside of NetworkX that we know of. It is based loosely on load_centrality in the sense that it counts the number of shortest paths which cross each edge. This function is for demonstration and testing purposes. Parameters ---------- G : graph A networkx graph cutoff : bool, optional (default=False) If specified, only consider paths of length <= cutoff. Returns ------- A dict keyed by edge 2-tuple to the number of shortest paths which use that edge. Where more than one path is shortest the count is divided equally among paths. r )r)edges_edge_betweennessr)) rrrurrre ubetweenvs rrrs0K ""1! QF! QF(($Qv>>>$NN,, ( (LAy NNNi 'NNNN ( rc:tj|||d\}}dt|t dD}i}||D]\}} d||| f<d|| |f<|r|} | |vr~t|| } || D]`} | |vrZt|| } || D]<} || | fxx|| | f| z z cc<|| | fxx|| | f| z z cc<=a||S)zEdge betweenness helper.Trcg|]\}}|Sr r )r!nds rr$z%_edge_betweenness..s F F FDAqa F F Frr )keyr )r&r'sortedr)rr4r+r,) rrnodesrr-r.r/r0r6rr1wr2s rr5r5s_^Avf$OOONT6 F FF6<<>>z!}}EEE F F FFG1AA  G JJLL 99DG I!W G G99 #DG I!!WGGA7Aq6?Y+FFA7Aq6?Y+FF  G Nr)NNTN)FTN)F)NF) __doc__operatorrnetworkxr&__all__ _dispatchablerr rrr5r rrrFs 4 5X&&&HHH'&HV0000f0    Fr