Properties of a random attachment growing network

TL;DR

This paper introduces a growing network model where nodes connect probabilistically, revealing a phase transition for giant component formation and differing behaviors depending on the number of potential partners.

Contribution

The study analyzes the structural properties of a new network growth model, highlighting phase transitions and the impact of the number of potential connections.

Findings

Giant component appears at a specific delta depending on k.

Average component size diverges at delta ≥ 0.5.

Network behavior varies significantly for k=1.

Abstract

In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects 'k' possible partners from the existing network and joins them with probability delta by undirected edges. The 'activity' of the node ends here; it will get new partners only if it is selected by a newcomer. The model produces an infinite-order phase transition when a giant component appears at a specific value of delta, which depends on k. The average component size is discontinuous at the transition. In contrast, the network behaves significantly different for k=1. There is no giant component formed for any delta and thus in this sense there is no phase transition. However, the average component size diverges for delta greater or equal than one half.