Scaling exponents and clustering coefficients of a growing random network

TL;DR

This paper investigates the properties of a growing scale-free network with constraints, revealing scaling exponents, clustering coefficients, and small-world characteristics through simulations.

Contribution

It extends a previous network model by incorporating constraints and analyzes resulting structural properties via simulations.

Findings

Scaling exponents between 1 and 2

Clustering coefficient $C_{out}$ around 0.1

Out-degree distribution exhibits exponential cutoff

Abstract

The statistical property of a growing scale-free network is studied based on an earlier model proposed by Krapivsky, Rodgers, and Redner [Phys. Rev. Lett. 86, 5401 (2001)], with the additional constraints of forbidden of self-connection and multiple links of the same direction between any two nodes. Scaling exponents in the range of 1-2 are obtained through Monte Carlo simulations and various clustering coefficients are calculated, one of which, $C_{\rm out}$, is of order $10^{-1}$, indicating the network resembles a small-world. The out-degree distribution has an exponential cut-off for large out-degree.