trophic_levels

trophic_levels(G, weight='weight')

Compute the trophic levels of nodes.

The trophic level of a node \(i\) is

\[s_i = 1 + \frac{1}{k^{in}_i} \sum_{j} a_{ij} s_j\]

where \(k^{in}_i\) is the in-degree of i

\[k^{in}_i = \sum_{j} a_{ij}\]

and nodes with \(k^{in}_i = 0\) have \(s_i = 1\) by convention.

These are calculated using the method outlined in Levine [1].

Parameters:

GDiGraph

A directed networkx graph

Returns:

nodesdict

Dictionary of nodes with trophic level as the value.

References

[1]

Stephen Levine (1980) J. theor. Biol. 83, 195-207