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We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…
We consider a random partition of the vertex set of an arbitrary graph that can be sampled using loop-erased random walks stopped at a random independent exponential time of parameter $q>0$, that we see as a tuning parameter.The related…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…
We study typical distances in a geometric random graph on the hyperbolic plane. Introduced by Krioukov et al.~\cite{ar:Krioukov} as a model for complex networks, $N$ vertices are drawn randomly within a bounded subset of the hyperbolic…
In the subgraph-freeness problem, we are given a constant-size graph $H$, and wish to determine whether the network contains $H$ as a subgraph or not. The \emph{property-testing} relaxation of the problem only requires us to distinguish…
Motivated by an application in community detection, we consider an \ER random graph conditioned on the rare event that all connected components are fully connected. Such graphs can be considered as partitions of vertices into cliques.…
We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p=c/n scaling for G(n,p)…
Community detection refers to the problem of clustering the nodes of a network (either graph or hypergrah) into groups. Various algorithms are available for community detection and all these methods apply to uncensored networks. In…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or…
We develop a general procedure that finds recursions for statistics counting isomorphic copies of a graph $G_0$ in the common random graph models ${\cal G}(n,m)$ and ${\cal G}(n,p)$. Our results apply when the average degrees of the random…
In this paper, we consider the hypothesis testing of correlation between two $m$-uniform hypergraphs on $n$ unlabelled nodes. Under the null hypothesis, the hypergraphs are independent, while under the alternative hypothesis, the hyperdges…
Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations.…
Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the…
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows to apply methods of complex network theory for characterizing time series. In this work we present the…
We consider the complexity of finding weighted homomorphisms from intersection graphs of curves (string graphs) with $n$ vertices to a fixed graph $H$. We provide a complete dichotomy for the problem: if $H$ has no two vertices sharing two…
We propose inhomogeneous random K-out graphs $\mathbb{H}(n; \pmb{\mu}, \pmb{K}_n)$, where each of the $n$ nodes is assigned to one of $r$ classes independently with a probability distribution $\pmb{\mu} = \{\mu_1, \ldots, \mu_r\}$. In…
As a fundamental structure in real-world networks, in addition to graph topology, communities can also be reflected by abundant node attributes. In attributed community detection, probabilistic generative models (PGMs) have become the…