shSrSSKrSSKJr /SQr\"S5\R "SS9S Sj55r\"S5\R "SS9S S j55r\"S5\R "SS9S S j55r g) zTrophic levelsN)not_implemented_for)trophic_levelstrophic_differencestrophic_incoherence_parameter undirectedweight) edge_attrsc URVVs/sHup#US:XdM UPM nnnU(d[R"S5e[R"XS9VVs1sH oUHofiM M nnn[ U5[ UR 5:wa[R"S5eSSKn[R"XS9RR5n URU SS9n XS:gSS2U S:g4n XU S:gSS2UR4- n U RSn URU 5n URRX- 5nURSS9S-n0nS UR5nUHnSUU'M S UR5n[#U5Hun nUR%U 5UU'M U$s snnfs snnf!URR anSn[R"U5UeSnAff=f) 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 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)axisc3:# UHupUS:XdM Uv M g7frN.0node_iddegrees z/Users/tiagomarins/Projetos/claudeai/copy_bank/venv/lib/python3.13/site-packages/networkx/algorithms/centrality/trophic.py !trophic_levels..[sOK6Q;WWK  c3:# UHupUS:wdM Uv M g7frrrs rrr`sR{OGfPQk{r) in_degreenx NetworkXError bfs_layerslennodesnumpyadjacency_matrixTtoarraysumnewaxisshapeeyelinalginv LinAlgError enumerateitem)Grndeg basal_nodeslayernodereachable_nodesnparowsumpnnierrmsgylevels zero_node_idsrnonzero_node_idss rrr s H$%;;;;#(1;K;  N  --??EDE? ?s177|+ P   A-//779AVVAAV F A+q&A+~&A 6Q; 2:: ..A B r A - IIMM!%  1 A FPAKKOM w!Sq{{R 01 7&&)w2 Mo<4 99 - ) s#,-s( G G G9GH /HH c`[XS9n0nURHupEX%X$- X4U4'M U$)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 )redges)r.rr>diffsuvs rrrgs<8A -F E FI-!f  Lc4SSKnU(a [XS9nOS[[R"U55nU(a"UR 5nUR U5 OUn[XaS9n[UR[UR5555$)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" rNr ) r!rlistrselfloop_edgescopyremove_edges_fromfloatstdvalues)r.r cannibalismr5rC self_loopsG_2s rrrsw8#A5"++A./ &&(C  ! !* -C#C7 U\\^,- ..rFr )rF) __doc__networkxrnetworkx.utilsr__all__ _dispatchablerrrrrFrrWs. T\"X&Y'#Yx\"X&'#B\"X&)/'#)/rF