U md@s\dZddlZddlmZdddgZedd d dZeddd dZeddd dZdS)zTrophic levelsN)not_implemented_fortrophic_levelstrophic_differencestrophic_incoherence_parameterZ undirectedweightc Cs.ddl}tj||dj}|j|dd}||dkdd|dkf}|||dkdd|jf}|jd}||}z|j ||}Wn6|j j k r} zd} t | | W5d} ~ XYnX|jddd} i} dd|j D} | D] }d| |<qd d|j D}t|D]\}}| || |<q| S) 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)ZaxiszTrophic levels are only defined for graphs where every node has a path from a basal node (basal nodes are nodes with no incoming edges).css|]\}}|dkr|VqdSrN.0node_idZdegreer r _/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/networkx/algorithms/centrality/trophic.py Gsz!trophic_levels..css|]\}}|dkr|VqdSr r r r r rrLs)numpynxZadjacency_matrixTZtoarraysumZnewaxisshapeeyeZlinalginvZ LinAlgErrorZ NetworkXErrorZ in_degree enumerate)GrnpaZrowsumpnninerrmsgylevelsZ zero_node_idsr Znonzero_node_idsr r rrs,"   cCs<t||d}i}|jD] \}}|||||||f<q|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)rrr"diffsuvr r rrSs  FcCsbddl}|rt||d}n6tt|}|r@|}||n|}t||d}|t|S)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) rrlistrZselfloop_edgescopyZremove_edges_fromZstdvalues)rrZ cannibalismrr$Z self_loopsZG_2r r rrus  )r)r)rF) __doc__ZnetworkxrZnetworkx.utilsr__all__rrrr r r rs   J !