U 9v fÉã@sTdZddlZddlmZddgZedƒedƒdd„ƒƒZedƒedƒd d„ƒƒZdS) z Communicability. éN)Únot_implemented_forÚcommunicabilityÚcommunicability_expZdirectedZ multigraphcCsæddl}t|ƒ}t ||¡}d||dk<|j |¡\}}| |¡}tt|t t |ƒƒƒƒ}i}|D]€} i|| <|D]n} d} || } || } t t |ƒƒD]8}| |dd…|f| |dd…|f| ||7} q”t | ƒ|| | <qpq`|S)a—Returns 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) rNéç) ZnumpyÚlistÚnxÚto_numpy_arrayÚlinalgZeighÚexpÚdictÚzipÚrangeÚlenÚfloat)ÚGÚnpÚnodelistÚAÚwZvecZexpwÚmappingÚcÚuÚvÚsÚpÚqÚj©rúK/tmp/pip-unpacked-wheel-_lngutwb/networkx/algorithms/communicability_alg.pyr s$:   6c Cs–ddl}ddl}t|ƒ}t ||¡}d||dk<|j |¡}tt|t t |ƒƒƒƒ}i}|D]6}i||<|D]$} t ||||| fƒ||| <qjqZ|S)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) rNrr) ÚscipyZ scipy.linalgrrr r Zexpmr r rrr) rÚspr rrZexpArrrrrrrr[s7   $)Ú__doc__ZnetworkxrZnetworkx.utilsrÚ__all__rrrrrrÚs  O