Log-Networks

TL;DR

This paper introduces a new growing network model where nodes attach to a target node and its ancestors, resulting in a sparse, ultra-small network with unique degree distributions and diameter, applicable to real-world networks like the Internet.

Contribution

The paper presents a novel network growth mechanism and analyzes its properties, providing insights into real networks with slow degree growth over time.

Findings

Average node degree grows logarithmically with network size

Network diameter remains constant at 2

Model predictions match real networks like the Internet and citation networks

Abstract

We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows logarithmically with network size while the network diameter equals 2. We determine basic geometrical network properties, such as the size dependence of the number of links and the in- and out-degree distributions. We also compare our predictions with real networks where the node degree also grows slowly with time -- the Internet and the citation network of all Physical Review papers.