A New Generative Statistical Model for Graphs: The Latent Order Logistic (LOLOG) Model

TL;DR

The paper introduces the Latent Order Logistic (LOLOG) model, a flexible probabilistic framework for complex networks, capable of modeling diverse graph distributions and addressing limitations of existing models.

Contribution

It presents the LOLOG model family, develops inference methods, and demonstrates its flexibility and advantages over existing models like ERGMs.

Findings

LOLOG can model scale-free networks via preferential attachment.

LOLOG avoids degeneracy and simplifies sampling.

Connections with ERGMs are established, showing equivalence under dyadic independence.

Abstract

Full probability models are critical for the statistical modeling of complex networks, and yet there are few general, flexible and widely applicable generative methods. We propose a new family of probability models motivated by the idea of network growth, which we call the Latent Order Logistic (LOLOG) model. LOLOG is a fully general framework capable of describing any probability distribution over graph configurations, though not all distributions are easily expressible or estimable as a LOLOG. We develop inferential procedures based on Monte Carlo Method of Moments, Generalized Method of Moments and variational inference. To show the flexibility of the model framework, we show how so-called scale-free networks can be modeled as LOLOGs via preferential attachment. The advantages of LOLOG in terms of avoidance of degeneracy, ease of sampling, and model flexibility are illustrated. Connections with the popular Exponential-family Random Graph model (ERGM) are also explored, and we find that they are identical in the case of dyadic independence. Finally, we apply the model to a social network of collaboration within a corporate law firm, a friendship network among adolescent students, and the friendship relations in an online social network.