hGSrSSKrSSKJr /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_attrscSSKn[R"XS9RR 5nUR USS9nX4S:gSS2US:g4nXTUS:gSS2UR 4- nURSnURU5nURRXu- 5nUR SS9S-n 0n SUR5n U HnSX'M SUR5n[U5Hup~U RU5X'M U $!URRan Sn [R"U 5U eSn A ff=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 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:# UHupUS:XdM Uv M g7frN.0node_iddegrees X/var/www/html/env/lib/python3.13/site-packages/networkx/algorithms/centrality/trophic.py !trophic_levels..IsOK6Q;WWK  c3:# UHupUS:wdM Uv M g7frrrs rrrNsR{OGfPQk{r)numpynxadjacency_matrixTtoarraysumnewaxisshapeeyelinalginv LinAlgError NetworkXError in_degree enumerateitem)Grnparowsumpnninerrmsgylevels zero_node_idsrnonzero_node_idss rrr sZF A-//779AVVAAV F A+q&A+~&A 6Q; 2:: ..A B r A - IIMM!%  1 A FPAKKOM !Sq{{R 01 &&)2 M- 99 - ) s#,-sDE5EEc`[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*rr5diffsuvs rrrUs<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 ) rrlistrselfloop_edgescopyremove_edges_fromfloatstdvalues)r*r cannibalismr+r: self_loopsG_2s rrrxsw8#A5"++A./ &&(C  ! !* -C#C7 U\\^,- ..r=r )rF) __doc__networkxrnetworkx.utilsr__all__ _dispatchablerrrrr=rrNs. T\"X&G'#GT\"X&'#B\"X&)/'#)/r=