A preferential attachment model with Poisson growth for scale-free networks

TL;DR

This paper introduces a flexible scale-free network model with Poisson growth, allowing for adjustable power-law exponents, and provides a probabilistic framework suitable for Bayesian inference applications.

Contribution

It extends the Barabási-Albert model by incorporating Poisson-distributed edges, enabling the generation of a wider variety of scale-free networks with tunable properties.

Findings

The model can produce networks with any power-law exponent.

A formula for network probability under the model is derived.

The model is applicable in Bayesian network inference.

Abstract

We propose a scale-free network model with a tunable power-law exponent. The Poisson growth model, as we call it, is an offshoot of the celebrated model of Barab\'{a}si and Albert where a network is generated iteratively from a small seed network; at each step a node is added together with a number of incident edges preferentially attached to nodes already in the network. A key feature of our model is that the number of edges added at each step is a random variable with Poisson distribution, and, unlike the Barab\'{a}si-Albert model where this quantity is fixed, it can generate any network. Our model is motivated by an application in Bayesian inference implemented as Markov chain Monte Carlo to estimate a network; for this purpose, we also give a formula for the probability of a network under our model.