Mercurial > repos > shellac > sam_consensus_v3
diff env/lib/python3.9/site-packages/networkx/algorithms/centrality/trophic.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/env/lib/python3.9/site-packages/networkx/algorithms/centrality/trophic.py Mon Mar 22 18:12:50 2021 +0000 @@ -0,0 +1,168 @@ +"""Trophic levels""" +import networkx as nx + +from networkx.utils import not_implemented_for + +__all__ = ["trophic_levels", "trophic_differences", "trophic_incoherence_parameter"] + + +@not_implemented_for("undirected") +def trophic_levels(G, weight="weight"): + r"""Compute 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 vale. + + References + ---------- + .. [1] Stephen Levine (1980) J. theor. Biol. 83, 195-207 + """ + try: + import numpy as np + except ImportError as e: + raise ImportError("trophic_levels() requires NumPy: http://numpy.org/") from e + + # find adjacency matrix + a = nx.adjacency_matrix(G, weight=weight).T.toarray() + + # drop rows/columns where in-degree is zero + rowsum = np.sum(a, axis=1) + p = a[rowsum != 0][:, rowsum != 0] + # normalise so sum of in-degree weights is 1 along each row + p = p / rowsum[rowsum != 0][:, np.newaxis] + + # calculate trophic levels + nn = p.shape[0] + i = np.eye(nn) + try: + n = np.linalg.inv(i - p) + except np.linalg.LinAlgError as err: + # LinAlgError is raised when there is a non-basal node + msg = ( + "Trophic levels are only defined for graphs where every " + + "node has a path from a basal node (basal nodes are nodes " + + "with no incoming edges)." + ) + raise nx.NetworkXError(msg) from err + y = n.sum(axis=1) + 1 + + levels = {} + + # all nodes with in-degree zero have trophic level == 1 + zero_node_ids = (node_id for node_id, degree in G.in_degree if degree == 0) + for node_id in zero_node_ids: + levels[node_id] = 1 + + # all other nodes have levels as calculated + nonzero_node_ids = (node_id for node_id, degree in G.in_degree if degree != 0) + for i, node_id in enumerate(nonzero_node_ids): + levels[node_id] = y[i] + + return levels + + +@not_implemented_for("undirected") +def trophic_differences(G, weight="weight"): + r"""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" + """ + levels = trophic_levels(G, weight=weight) + diffs = {} + for u, v in G.edges: + diffs[(u, v)] = levels[v] - levels[u] + return diffs + + +@not_implemented_for("undirected") +def trophic_incoherence_parameter(G, weight="weight", cannibalism=False): + r"""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" + """ + try: + import numpy as np + except ImportError as e: + raise ImportError( + "trophic_incoherence_parameter() requires NumPy: " "http://scipy.org/" + ) from e + + if cannibalism: + diffs = trophic_differences(G, weight=weight) + else: + # If no cannibalism, remove self-edges + self_loops = list(nx.selfloop_edges(G)) + if self_loops: + # Make a copy so we do not change G's edges in memory + G_2 = G.copy() + G_2.remove_edges_from(self_loops) + else: + # Avoid copy otherwise + G_2 = G + diffs = trophic_differences(G_2, weight=weight) + return np.std(list(diffs.values()))