arXiv subjects

Watson Levens

Publications and source records attributed to Watson Levens.

2 recordsLinked to original sources

arXiv2024

Properties of the `friend of a friend' model for network generation

The way in which a social network is generated, in terms of how individuals attach to each other, determines the properties of the resulting network. Here we study an intuitively appealing `friend of a friend' model, where a network is formed by each newly added individual attaching first to a randomly chosen target and then to $n_q\geq 1$ randomly chosen friends of the target, each with probability $0<q\leq1$. We revisit the master equation of the expected degree distribution for this model, providing an exact solution for the case when $n_q$ allows for attachment to all of the chosen target's friends (a case previously studied by \cite{lambiotte2016}), and demonstrating why such a solution is hard to obtain when $n_q$ is fixed (a case previously studied by \cite{Levens2022}.) In the case where attachment to all friends is allowed, we also show that when $q<q^*\approx0.5671$, the expected degree distribution of the model is stationary as the network size tends to infinity. We go on to look at the clustering behaviour and the triangle count, focusing on the cases where $n_q$ is fixed.

physics.soc-ph↗

arXiv2022

Friend of a friend models of network growth

One of the best-known models in network science is preferential attachment. In this model, the probability of attaching to a node depends on the degree of all nodes in the population, and thus depends on global information. In many biological, physical, and social systems, however, interactions between individuals depend only on local information. Here, we investigate a truly local model of network formation, based on the idea of a friend of a friend, with the following rule: individuals choose one node at random and link to it with probability p, then they choose a neighbour of that node and link with probability q. Our model produces power laws with empirical exponents ranging from 1.5 upwards and clustering co-efficients ranging from 0 up to 0.5 (consistent with many real networks). For small p and q=1, the model produces super-hub networks, and we prove that for p=0 and q=1, the proportion of non-hubs tends to 1 as the network grows. We show that power-law degree distributions, small world clustering and super-hub networks are all outcomes of this, more general, yet conceptually simple model.

physics.soc-ph↗