VhdZddlZddlmZgdZedej dd dZedej dd d Zedej dd d Z y) zTrophic levelsN)not_implemented_for)trophic_levelstrophic_differencestrophic_incoherence_parameter undirectedweight) edge_attrsc|jDcgc] \}}|dk(s |}}}|stjdtj||Dchc] }|D]}| }}}t |t |j k7rtjdddl}tj||jj} |j| d} | | dk7dd| dk7f} | | | dk7dd|jfz } | jd} |j| } |jj| | z }|jddz}i}d |jD}|D]}d||< d |jD}t#|D]\} }|j%| ||<|Scc}}wcc}}w#|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 rz|This graph has no basal nodes (nodes with no incoming edges).Trophic levels are not defined without at least one basal node.)sourceszTrophic levels are only defined for graphs where every node has a path from a basal node (basal nodes are nodes with no incoming edges).Nr)axisc32K|]\}}|dk(s |ywrN.0node_iddegrees V/home/dcms/DCMS/lib/python3.12/site-packages/networkx/algorithms/centrality/trophic.py z!trophic_levels..[sO&6Q;WO c32K|]\}}|dk7s |ywrrrs rrz!trophic_levels..`sROGVfPQkRr) in_degreenx NetworkXError bfs_layerslennodesnumpyadjacency_matrixTtoarraysumnewaxisshapeeyelinalginv LinAlgError enumerateitem)Grndeg basal_nodeslayernodereachable_nodesnparowsumpnnierrmsgylevels zero_node_idsrnonzero_node_idss rrr s%H$%;;;C#(1;K;  N  --;?EDH O ?s177|+ P   Af-//779AVVAAV F &A+q&A+~&A F6Q; 2:: ..A B r A - IIMM!a%  1 A FPAKKOM wSq{{R 01$ 7&&)w$ Mo<4 99 - ) s#,-s( GGG 4GH)HHclt||}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-rr=diffsuvs rrrgsK8Af -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 ) r rlistrselfloop_edgescopyremove_edges_fromfloatstdvalues)r-r cannibalismr4rB self_loopsG_2s rrrs{8#Af5"++A./ &&(C  ! !* -C#C7 U\\^,- ..rEr )rF) __doc__networkxrnetworkx.utilsr__all__ _dispatchablerrrrrErrVs. T\"X&Y'#Yx\"X&'#B\"X&)/'#)/rE