## Mercurial > repos > shellac > sam_consensus_v3

### view env/lib/python3.9/site-packages/networkx/algorithms/centrality/trophic.py @ 0:4f3585e2f14b draft default tip

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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |

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"""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()))