Age-dependent random connection models with arc reciprocity: clustering and connectivity

TL;DR

This paper introduces a novel age-dependent directed network model with reciprocal connections, exhibiting power-law degree distributions and tunable outdegree, and analyzes its clustering, connectivity, and percolation properties.

Contribution

It presents a new spatial network model incorporating age-based reciprocity, linking finite and infinite models, and studies their structural and percolation characteristics.

Findings

The model produces power-law indegree distributions.

Reciprocal connections depend on age differences.

The infinite and finite models are locally convergent.

Abstract

We introduce a model for directed spatial networks. Starting from an age-based preferential attachment model in which all arcs point from younger to older vertices, we add \emph{reciprocal} connections whose probabilities depend on the age difference between their end-vertices. This yields a directed graph with reciprocal correlations, a power-law indegree distribution, and a tunable outdegree distribution. We consider two versions of the model: an infinite version embedded in $\mathbb{R}^d$, which can be constructed as a weight-dependent random connection model with a non-symmetric kernel, and a growing sequence of graphs on the unit torus that converges locally to the infinite model. Besides establishing the local limit result linking the two models, we investigate degree distributions, various directed clustering metrics, and directed percolation.