Estimating Formation Mechanisms and Degree Distributions in Mixed Attachment Networks

TL;DR

This paper introduces a method to estimate how different attachment mechanisms influence the growth of networks, using likelihood analysis and expectation maximization to accurately infer contributions and degree distributions.

Contribution

It develops a generic model for mixed attachment mechanisms, establishes conditions for likelihood analysis, and proves convergence of the EM algorithm for estimating mechanism contributions.

Findings

The EM algorithm converges to accurate estimates of attachment contributions.

In-degree distributions converge to stationary distributions in simulations.

Likelihood analysis guarantees local maxima under certain conditions.

Abstract

Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to random and preferential linkage with a fixed probability. Past approaches apply likelihood analysis to estimate the probability of occurrence of each mechanism at a particular network instance, exploiting the concavity of the likelihood function at each point in time. However, the probability of connecting to existing nodes, and consequently the likelihood function itself, varies as networks grow. We establish conditions under which applying likelihood analysis guarantees the existence of a local maximum of the time-varying likelihood function and prove that an expectation maximization algorithm provides a convergent estimate. Furthermore, the in-degree distributions of the nodes in the growing networks are analytically characterized. Simulations show that, under the proposed conditions, expectation maximization and maximum-likelihood accurately estimate the actual contribution of each mechanism, and in-degree distributions converge to stationary distributions.