Disassortativity of random critical branching trees

TL;DR

This paper analytically demonstrates that random critical branching trees exhibit disassortative degree-degree correlation, and this disassortativity is linked to the fractal scaling observed in complex networks.

Contribution

It provides an analytical proof of disassortativity in CBTs and connects this property to fractal scaling in complex networks.

Findings

CBTs are disassortative despite stochastic independence.

Skeletons of fractal networks behave similarly to CBT in DDC.

Disassortativity may underlie fractal scaling in complex networks.

Abstract

Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this stochastic independence, there exists the degree-degree correlation (DDC) in the CBT and it is disassortative. Moreover, the skeletons of fractal networks, the maximum spanning trees formed by the edge betweenness centrality, behave similarly to the CBT in the DDC. This analytic solution and observation support the argument that the fractal scaling in complex networks originates from the disassortativity in the DDC.