GddZddlZddlmZgdZedd dZedd dZedd d ZdS) zTrophic levelsN)not_implemented_for)trophic_levelstrophic_differencestrophic_incoherence_parameter undirectedweightcddl}tj||j}||d}||dkdd|dkf}|||dkdd|jfz }|jd}||} |j ||z }n.#|j j $r} d} tj | | d} ~ wwxYw|ddz} i} d|j D} | D]}d| |<d|j D}t|D]\}}| || |<| 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)axiszTrophic levels are only defined for graphs where every node has a path from a basal node (basal nodes are nodes with no incoming edges).c3,K|]\}}|dk |VdSrN.0node_iddegrees Flib/python3.11/site-packages/networkx/algorithms/centrality/trophic.py z!trophic_levels..Gs*OO&6Q;;W;;;;OOc3,K|]\}}|dk |VdSrrrs rrz!trophic_levels..Ls+RROGVfPQkkkkkkRRr)numpynxadjacency_matrixTtoarraysumnewaxisshapeeyelinalginv LinAlgError NetworkXError in_degree enumerate)Grnparowsumpnninerrmsgylevels zero_node_idsrnonzero_node_idss rrrsD Af---/7799AVVAAV  F &A+qqq&A+~&A F6Q; 2: ..A B r A - IMM!a%  9 --- ) s##,- 1 A FPOAKOOOM wSRq{RRR 011 7A$w Ms$CC-C((C-crt||}i}|jD]\}}||||z |||f<|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)r'rr2diffsuvs rrrSsQ6Af - - -F E..1q F1I-q!f LrFcZddl}|rt||}n`ttj|}|r*|}||n|}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 ) rrlistrselfloop_edgescopyremove_edges_fromstdvalues)r'r cannibalismr(r7 self_loopsG_2s rrrus6 8#Af555"+A..//  &&((C  ! !* - - - -C#C777 66$u||~~&& ' ''rr )rF) __doc__networkxrnetworkx.utilsr__all__rrrrrrrHs...... T T T\""GGG#"GT\""#"B\"")()()(#")()()(r