o ]ZhG@s~dZddlZddlmZgdZedejddddd Zedejdddd d Zedejdddd dZ dS)zTrophic levelsN)not_implemented_for)trophic_levelstrophic_differencestrophic_incoherence_parameterZ undirectedweight)Z edge_attrsc Cs$ddl}tj||dj}|j|dd}||dkdd|dkf}|||dkdd|jf}|jd}||}z |j ||}Wn|j j y\} zd} t | | d} ~ ww|jddd} i} dd|j D} | D]}d| |<qqd d|j D}t|D] \}}| || |<q| S) aCompute the trophic levels of nodes. The trophic level of a node $i$ is .. math:: s_i = 1 + \frac{1}{k^{in}_i} \sum_{j} a_{ij} s_j where $k^{in}_i$ is the in-degree of i .. math:: k^{in}_i = \sum_{j} a_{ij} and nodes with $k^{in}_i = 0$ have $s_i = 1$ by convention. These are calculated using the method outlined in Levine [1]_. Parameters ---------- G : DiGraph A directed networkx graph Returns ------- nodes : dict Dictionary of nodes with trophic level as the value. References ---------- .. [1] Stephen Levine (1980) J. theor. Biol. 83, 195-207 rNr)ZaxiszTrophic levels are only defined for graphs where every node has a path from a basal node (basal nodes are nodes with no incoming edges).css |] \}}|dkr|VqdSrN.0node_idZdegreer r U/var/www/auris/lib/python3.10/site-packages/networkx/algorithms/centrality/trophic.py Iz!trophic_levels..css |] \}}|dkr|VqdSr r r r r rrNr)numpynxZadjacency_matrixTZtoarraysumZnewaxisshapeeyeZlinalginvZ LinAlgErrorZ NetworkXErrorZ in_degree enumerateitem)GrnpaZrowsumpnninerrmsgylevelsZ zero_node_idsr Znonzero_node_idsr r rr s0#    rcCs<t||d}i}|jD]\}}|||||||f<q |S)asCompute the trophic differences of the edges of a directed graph. The trophic difference $x_ij$ for each edge is defined in Johnson et al. [1]_ as: .. math:: x_ij = s_j - s_i Where $s_i$ is the trophic level of node $i$. Parameters ---------- G : DiGraph A directed networkx graph Returns ------- diffs : dict Dictionary of edges with trophic differences as the value. References ---------- .. [1] Samuel Johnson, Virginia Dominguez-Garcia, Luca Donetti, Miguel A. Munoz (2014) PNAS "Trophic coherence determines food-web stability" r)redges)rrr$diffsuvr r rrUs rFcCsfddl}|r t||d}ntt|}|r |}||n|}t||d}t|t| S)a+Compute the trophic incoherence parameter of a graph. Trophic coherence is defined as the homogeneity of the distribution of trophic distances: the more similar, the more coherent. This is measured by the standard deviation of the trophic differences and referred to as the trophic incoherence parameter $q$ by [1]. Parameters ---------- G : DiGraph A directed networkx graph cannibalism: Boolean If set to False, self edges are not considered in the calculation Returns ------- trophic_incoherence_parameter : float The trophic coherence of a graph References ---------- .. [1] Samuel Johnson, Virginia Dominguez-Garcia, Luca Donetti, Miguel A. Munoz (2014) PNAS "Trophic coherence determines food-web stability" rNr) rrlistrZselfloop_edgescopyZremove_edges_fromfloatZstdvalues)rrZ cannibalismrr&Z self_loopsZG_2r r rrxs  rr)rF) __doc__ZnetworkxrZnetworkx.utilsr__all__Z _dispatchablerrrr r r rs  J !