Networks with growth and preferential attachment: modelling and applications

Abstract

This article presents a brief overview of the main network models that use growth and preferential attachment. We start with the classical model proposed by Barabási and Albert: nodes are added to the network connecting preferably to nodes that are more connected. We also present models that consider more representative elements from social perspectives, such as the homophily between the nodes and the fitness that each node has, to build connections. Furthermore, we show a version of these models that includes Euclidean distance between the nodes as a preferential attachment component. Our objective is to study the fundamental properties of these networks, as distribution of connectivity, degree correlation, shortest path, cluster coefficient and how these characteristics are affected by the preferential attachment rules. In addition to the review, we also provided an application of these models using real-world networks.