A Network Model Characterized by a Latent Attribute Structure with Competition

The quest for a model that is able to explain, describe, analyze and simulate real-world complex networks is of uttermost practical, as well as theoretical, interest. In fact, networks can be a natural way to represent many phenomena; often, they arise from a complex interweaving of some features of the nodes. For example, in a co-authorship network, a link stems more easily between authors with similar interests; similarly, in a genetic regulatory network, links are affected by the different biological functions of the regulators. In this paper we introduce and study a novel network model that is based on a latent attribute structure: this model, inspired by a generalization of the Indian buffet process, is simple and contains a small number of parameters, with a clear and intuitive role. Each node is characterized by a number of features and the probability of the existence of an edge between two nodes depends on the features they share; the number of possible features is not fixed a priori and can grow indefinitely. Moreover, a random fitness parameter is introduced for each node in order to determine its ability to transmit its own features to other nodes; this behavior is added on top of a process of Indian-Buffet type. Because of the fitness property, a node’s connectivity does not depend on its age alone, so that also “young but fit” nodes are able to compete and succeed in propagating their features and acquiring links. We also show how, considering the resulting bipartite node-attribute network, it is possible to gain some insight about which nodes were originally the most “fit”. Our model for this bipartite network depends on few parameters, that are characterized by their straightforward interpretation and by the availability of proper estimators. Even if the parameters are easy to interpret and tune, the model is general enough to represent complex phenomena - e.g., homophily, heterophily, or any interplay between features. We provide some theoretical as well as experimental results regarding the power-law behavior of the model and the proposed tools for the estimation of the parameters. We also show, through a number of experiments, how the proposed model naturally captures most local and global properties (e.g., degree distributions, connectivity and distance distributions) real networks exhibit.