Evolving Apollonian Networks with Small-world Scale-free topologies

TL;DR

This paper introduces two types of evolving networks, EAN and GDAN, demonstrating their power-law degree distributions, small-world properties, and synchronization behaviors through simulation and theoretical analysis.

Contribution

It presents new models of evolving Apollonian networks with tunable degree exponents and analyzes their structural properties and synchronization dynamics.

Findings

Both networks follow power-law degree distributions with exponents from 2 to 3.

Networks exhibit small-world features with low average path length and diameter.

Analytical expressions for clustering coefficients are provided.

Abstract

We propose two types of evolving networks: evolutionary Apollonian networks (EAN) and general deterministic Apollonian networks (GDAN), established by simple iteration algorithms. We investigate the two networks by both simulation and theoretical prediction. Analytical results show that both networks follow power-law degree distributions, with distribution exponents continuously tuned from 2 to 3. The accurate expression of clustering coefficient is also given for both networks. Moreover, the investigation of the average path length of EAN and the diameter of GDAN reveals that these two types of networks possess small-world feature. In addition, we study the collective synchronization behavior on some limitations of the EAN.