+ )iRt^RIt^RIHtRR.t]!R4]!R4]P R444t]!R4]!R4]P R444tR#) z Communicability. N)not_implemented_forcommunicabilitycommunicability_expdirected multigraphc 2^RIp\V4p\P!W4p^W3R8g&VPP V4wrEVP V4p\\V\\V4444p/pVFp /W&VFp ^p Wy,p Wz,p \\V44F?pWRV3,V ,VRV3,V ,,Wn,,, p KA \V 4W,V &K K V#)aReturns communicability between all pairs of nodes in G. The communicability between pairs of nodes in G is the sum of walks of different lengths starting at node u and ending at node v. Parameters ---------- G: graph Returns ------- comm: dictionary of dictionaries Dictionary of dictionaries keyed by nodes with communicability as the value. Raises ------ NetworkXError If the graph is not undirected and simple. See Also -------- communicability_exp: Communicability between all pairs of nodes in G using spectral decomposition. communicability_betweenness_centrality: Communicability betweenness centrality for each node in G. Notes ----- This algorithm uses a spectral decomposition of the adjacency matrix. Let G=(V,E) be a simple undirected graph. Using the connection between the powers of the adjacency matrix and the number of walks in the graph, the communicability between nodes `u` and `v` based on the graph spectrum is [1]_ .. math:: C(u,v)=\sum_{j=1}^{n}\phi_{j}(u)\phi_{j}(v)e^{\lambda_{j}}, where `\phi_{j}(u)` is the `u\rm{th}` element of the `j\rm{th}` orthonormal eigenvector of the adjacency matrix associated with the eigenvalue `\lambda_{j}`. References ---------- .. [1] Ernesto Estrada, Naomichi Hatano, "Communicability in complex networks", Phys. Rev. E 77, 036111 (2008). https://arxiv.org/abs/0707.0756 Examples -------- >>> G = nx.Graph([(0, 1), (1, 2), (1, 5), (5, 4), (2, 4), (2, 3), (4, 3), (3, 6)]) >>> c = nx.communicability(G) N:NNN) numpylistnxto_numpy_arraylinalgeighexpdictziprangelenfloat)GnpnodelistAwvecexpwmappingcuvspqjs& e/var/www/html/photoedit/myenv/lib/python3.14/site-packages/networkx/algorithms/communicability_alg.pyrr svAwH !&AA3hK YY^^A FA 66!9D3xs8}!567G A AA A A3x=)AYq\C1IaL047::*AhADG  Hc d^RIp\V4p\P!W4p^W3R8g&VPP V4p\ \V\\V4444p/pVF9p/Wg&VF,p\WEV,WX,3,4Wg,V&K. K; V#)a Returns communicability between all pairs of nodes in G. Communicability between pair of node (u,v) of node in G is the sum of walks of different lengths starting at node u and ending at node v. Parameters ---------- G: graph Returns ------- comm: dictionary of dictionaries Dictionary of dictionaries keyed by nodes with communicability as the value. Raises ------ NetworkXError If the graph is not undirected and simple. See Also -------- communicability: Communicability between pairs of nodes in G. communicability_betweenness_centrality: Communicability betweenness centrality for each node in G. Notes ----- This algorithm uses matrix exponentiation of the adjacency matrix. Let G=(V,E) be a simple undirected graph. Using the connection between the powers of the adjacency matrix and the number of walks in the graph, the communicability between nodes u and v is [1]_, .. math:: C(u,v) = (e^A)_{uv}, where `A` is the adjacency matrix of G. References ---------- .. [1] Ernesto Estrada, Naomichi Hatano, "Communicability in complex networks", Phys. Rev. E 77, 036111 (2008). https://arxiv.org/abs/0707.0756 Examples -------- >>> G = nx.Graph([(0, 1), (1, 2), (1, 5), (5, 4), (2, 4), (2, 3), (4, 3), (3, 6)]) >>> c = nx.communicability_exp(G) Nr) scipyr r r r expmrrrrr) rsprrexpArrrrs & r$rr]spAwH !&AA3hK 99>>! D3xs8}!567G A ADWZ!789ADG Hr%) __doc__networkxr networkx.utilsr__all__ _dispatchablerrr%r$r1s. 3 4Z \"L #!L ^Z \"C #!C r%