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Exponential-family random graph models (ERGMs) are a family of network modelsoriginating in social network analysis, which have also been applied tobiological networks. Advances in estimation algorithms have increased thepractical scope of these models to larger networks, however it is still notalways possible to estimate a model without encountering problems of modelnear-degeneracy, particularly if it is desired to use only simple modelparameters, rather than more complex parameters designed to overcome theproblem of near-degeneracy. Two new network models related to the ERGM, theTapered ERGM, and the latent order logistic (LOLOG) model, have recently beenproposed to overcome this problem. In this work I illustrate the application ofthe Tapered ERGM and the LOLOG to a set of biological networks, includingprotein-protein interaction (PPI) networks, gene regulatory networks, andneural networks. I find that the Tapered ERGM and the LOLOG are able toestimate models for networks for which it was not possible to estimate aconventional ERGM, and are able to do so using only simple model parameters. Inthe case of two neural networks where data on the spatial position of neuronsis available, this allows the estimation of models including terms for spatialdistance and triangle structures, allowing triangle motif statisticalsignificance to be estimated while accounting for the effect of spatialproximity on connection probability. For some larger networks, however, TaperedERGM and LOLOG estimation was not possible in practical time, whileconventional ERGM models were able to be estimated only by using theEquilibrium Expectation (EE) algorithm.

New network models facilitate analysis of biological networks