A Markov Chain-Based Numerical Method for Calculating Network Degree Distributions

TL;DR

This paper introduces a Markov chain-based numerical method to efficiently compute degree distributions in scale-free networks, specifically under the BA model, with demonstrated accuracy and improved computational complexity.

Contribution

It establishes a novel relation between scale-free networks and Markov chains and develops an efficient algorithm for degree distribution calculation.

Findings

The algorithm has a complexity of O(t^2).

Results agree with existing methods.

Demonstrated on three example networks.

Abstract

This paper establishes a relation between scale-free networks and Markov chains, and proposes a computation framework for degree distributions of scale-free networks. We first find that, under the BA model, the degree evolution of individual nodes in a scale-free network follows some non-homogeneous Markov chains. Exploring the special structure of these Markov chains, we are able to develop an efficient algorithm to compute the degree distribution numerically. The complexity of our algorithm is O(t^2), where $t$ is the number of time steps for adding new nodes. We use three examples to demonstrate the computation procedure and compare the results with those from the existing methods.