+ )i Rt^RIt^RIHt.R Ot]!R4]P !RR7R Rl44t]!R4]P !RR7R Rl44t]!R4]P !RR7R Rl44t R#) zTrophic levelsN)not_implemented_for undirectedweight) edge_attrscrVPUUu.uFwr#V^8XgKVNK pppV'g\P!R4h\P!WR7UUu0uF qUFqfkK K ppp\ V4\ VP 48wd\P!R4h^RIp\P!WR7PP4p VPV ^R7p W^8g,RV ^8g3,p WV ^8g,RVP3,, p V P^,p VPV 4p VPPW, 4pTP^R7^,p/pRTP4pTFp^TT&K R TP4p\#T4Fwp pTP%T 4TT&K T#uuppiuuppi TPP dpRp\P!T4ThRp?ii;i) aBCompute 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 z|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)axis:NNNc3<"TFwrV^8XgKVxK R#5iN.0node_iddegrees& d/var/www/html/photoedit/myenv/lib/python3.14/site-packages/networkx/algorithms/centrality/trophic.py !trophic_levels..[sOK6Q;WWK  c3<"TFwrV^8wgKVxK R#5ir r rs& rrr`sR{OGfPQk{r) in_degreenx NetworkXError bfs_layerslennodesnumpyadjacency_matrixTtoarraysumnewaxisshapeeyelinalginv LinAlgError enumerateitem)Grndeg basal_nodeslayernodereachable_nodesnparowsumpnnierrmsgylevels zero_node_idsrnonzero_node_idss&& rtrophic_levelsr= s H$%;;;;#(11;K;  N  --??EDE? ?s177|+ P   A-//779AVVAAV F A+q&A+~&A 6Q; 2:: ..A B r A - IIMM!%  1 A FPAKKOM w!Sq{{R 01 7&&)w2 Mo<4 99 - ) s#,-s( G1G1!G7!G==H6H11H6c~\WR7p/pVPFwrEW%,W$,, W4V3&K V#)a+Compute 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)r=edges)r*rr:diffsuvs&& rtrophic_differencesrCgs<8A -F E FI-!f  LcD^RIpV'd\WR7pMW\\P!V44pV'd#VP 4pVP V4MTp\WaR7p\VP\VP4444#)aCompute 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" Nr) rrClistrselfloop_edgescopyremove_edges_fromfloatstdvalues)r*r cannibalismr1r@ self_loopsG_2s&&& rtrophic_incoherence_parameterrPsw8#A5"++A./ &&(C  ! !* -C#C7 U\\^,- ..rD)r=rCrPr)rF) __doc__networkxrnetworkx.utilsr__all__ _dispatchabler=rCrPr rDrrVs. T\"X&Y'#Yx\"X&'#B\"X&)/'#)/rD