New network models facilitate analysis of biological networks

TL;DR

This paper demonstrates that the Tapered ERGM and LOLOG models can successfully analyze larger biological networks, overcoming limitations of traditional ERGMs, and incorporate spatial and structural features in network modeling.

Contribution

The work introduces practical applications of Tapered ERGM and LOLOG to biological networks, enabling estimation with simple parameters where traditional ERGMs fail.

Findings

Tapered ERGM and LOLOG estimate models for larger biological networks.

These models incorporate spatial distance and triangle motifs.

Traditional ERGMs require specialized algorithms like EE for larger networks.

Abstract

Exponential-family random graph models (ERGMs) are a family of network models originating in social network analysis, which have also been applied to biological networks. Advances in estimation algorithms have increased the practical scope of these models to larger networks, however it is still not always possible to estimate a model without encountering problems of model near-degeneracy, particularly if it is desired to use only simple model parameters, rather than more complex parameters designed to overcome the problem of near-degeneracy. Two new network models related to the ERGM, the Tapered ERGM, and the latent order logistic (LOLOG) model, have recently been proposed to overcome this problem. In this work I illustrate the application of the Tapered ERGM and the LOLOG to a set of biological networks, including protein-protein interaction (PPI) networks, gene regulatory networks, and neural networks. I find that the Tapered ERGM and the LOLOG are able to estimate models for networks for which it was not possible to estimate a conventional ERGM, and are able to do so using only simple model parameters. In the case of two neural networks where data on the spatial position of neurons is available, this allows the estimation of models including terms for spatial distance and triangle structures, allowing triangle motif statistical significance to be estimated while accounting for the effect of spatial proximity on connection probability. For some larger networks, however, Tapered ERGM and LOLOG estimation was not possible in practical time, while conventional ERGM models were able to be estimated only by using the Equilibrium Expectation (EE) algorithm.