Statistics of leaders and lead changes in growing networks

TL;DR

This paper analyzes the statistical properties of leaders in growing networks, focusing on degree distribution, lead changes, and leader identity across different attachment models.

Contribution

It provides a comprehensive analysis of leader statistics and lead change dynamics in various stochastic network growth models.

Findings

Distribution of leader degrees characterized

Number of lead changes quantified

Leader persistence probabilities computed

Abstract

We investigate various aspects of the statistics of leaders in growing network models defined by stochastic attachment rules. The leader is the node with highest degree at a given time (or the node which reached that degree first if there are co-leaders). This comprehensive study includes the full distribution of the degree of the leader, its identity, the number of co-leaders, as well as several observables characterizing the whole history of lead changes: number of lead changes, number of distinct leaders, lead persistence probability. We successively consider the following network models: uniform attachment, linear attachment (the Barabasi-Albert model), and generalized preferential attachment with initial attractiveness.