ިsgGdZddlZddlmZgdZedej dd dZedej dd d Zedej dd d Z y) zTrophic levelsN)not_implemented_for)trophic_levelstrophic_differencestrophic_incoherence_parameter undirectedweight) edge_attrscddl}tj||jj }|j |d}||dk7dd|dk7f}|||dk7dd|j fz }|jd}|j|} |jj||z }|j ddz} i} d|jD} | D]}d| |< d|jD}t|D]\}}| j|| |<| S#|jj$r} d} tj| | d} ~ wwxYw) 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).c32K|]\}}|dk(s |ywrN.0node_iddegrees Y/var/www/html/venv/lib/python3.12/site-packages/networkx/algorithms/centrality/trophic.py z!trophic_levels..IsO&6Q;WO c32K|]\}}|dk7s |ywrrrs rrz!trophic_levels..NsROGVfPQkRr)numpynxadjacency_matrixTtoarraysumnewaxisshapeeyelinalginv LinAlgError NetworkXError in_degree enumerateitem)Grnparowsumpnninerrmsgylevels zero_node_idsrnonzero_node_idss rrr srF Af-//779AVVAAV F &A+q&A+~&A F6Q; 2:: ..A B r A - IIMM!a%  1 A FPAKKOM wSq{{R 01$ 7&&)w$ M- 99 - ) s#,-sD&&E?EEclt||}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)rr4diffsuvs rrrUsK8Af -F E.1q F1I-q!f . Lc.ddl}|rt||}nQttj|}|r"|j }|j |n|}t||}t|jt|jS)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_fromfloatstdvalues)r)r cannibalismr*r9 self_loopsG_2s rrrxs{8#Af5"++A./ &&(C  ! !* -C#C7 U\\^,- ..r<r )rF) __doc__networkxrnetworkx.utilsr__all__ _dispatchablerrrrr<rrMs. T\"X&G'#GT\"X&'#B\"X&)/'#)/r<