Causal and homogeneous networks

TL;DR

This paper explores how causality influences the structure and properties of growing networks, revealing that causal networks tend to have shorter average distances and can develop singular nodes under certain conditions.

Contribution

It demonstrates the significant impact of causality on network scaling, geometry, and degree distribution stability, providing a solvable model and theoretical insights.

Findings

Causal networks have smaller average distances than homogeneous networks.

Surplus links can cause the emergence of a singular node with degree proportional to total links.

Causality affects the stability of scale-free degree distributions.

Abstract

Growing networks have a causal structure. We show that the causality strongly influences the scaling and geometrical properties of the network. In particular the average distance between nodes is smaller for causal networks than for corresponding homogeneous networks. We explain the origin of this effect and illustrate it using as an example a solvable model of random trees. We also discuss the issue of stability of the scale-free node degree distribution. We show that a surplus of links may lead to the emergence of a singular node with the degree proportional to the total number of links. This effect is closely related to the backgammon condensation known from the balls-in-boxes model.