A spectral graph theoretic study of predator-prey networks

TL;DR

This study uses spectral graph theory to differentiate predator-prey networks from aqueous and terrestrial environments, revealing that their structural differences are due to edge orientation rather than randomness, with no universal pattern across environments.

Contribution

The paper introduces a spectral graph theoretic approach to distinguish predator-prey networks based on environment, highlighting the role of edge orientation in structural differences.

Findings

Spectral analysis differentiates aquatic and terrestrial predator-prey networks.

Edge orientation, not randomness, explains structural differences.

No universal structural pattern exists across different environments.

Abstract

Predator-prey networks originating from different aqueous and terrestrial environments are compared to assess if the difference in environments of these networks produce any significant difference in the structure of such predator-prey networks. Spectral graph theory is used firstly to discriminate between the structure of such predator-prey networks originating from aqueous and terrestrial environments and secondly to establish that the difference observed in the structure of networks originating from these two environments are precisely due to the way edges are oriented in these networks and are not a property of random networks.We use random projections in $\mathbb{R^2}$ and $\mathbb{R^3}$ of weighted spectral distribution (WSD) of the networks belonging to the two classes viz. aqueous and terrestrial to differentiate between the structure of these networks. The spectral theory of graph non-randomness and relative non-randomness is used to establish the deviation of structure of these networks from having a topology similar to random networks.We thus establish the absence of a universal structural pattern across predator-prey networks originating from different environments.