Limiting Degree Distribution for a Sublinear Preferential Attachment Model with Communities

Seed Seminar of Mathematics and Physics
Fall’ 25: Random Forests and Fermionic Field Theories 
For many real-world networks, such as the World Wide Web, the degree distribution follows a power law. It is therefore useful to have simple random graph models whose limiting degree distribution exhibits this same feature. With this motivation, physicists Albert-László Barabási and Réka Albert introduced the preferential attachment model that now bears their name. A further advantage of this model is that it incorporates temporal dynamics: starting from an initial graph $mathcal{G}_0$, the graph at time $n+1$ is obtained from the graph at time $n$, denoted $mathcal{G}_n$, by adding a new vertex $v_{n+1}$. This vertex then attaches to one or several vertices of $mathcal{G}_n$ according to a preferential attachment rule, meaning that the probability of connecting to a given vertex of $mathcal{G}_n$ is proportional to its degree.
We present an extension of this model in which each vertex of the graph is assigned a community (or type), and in which the preferential attachment is sublinear; that is, the probability of attaching to a vertex $u$ is proportional to $deg(u)^gamma$, where $gamma$ is a parameter taking values in $(0,1)$.
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.