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Graph Neural Networks (GNNs) have improved unsupervised community detection of clustered nodes due to their ability to encode the dual dimensionality of the connectivity and feature information spaces of graphs. Identifying the latent…
Let $\{G_n\}_1^{\infty}$ be a sequence of non-trivial finite groups. In this paper, we study the properties of a random walk on the complete monomial group $G_n\wr S_n$ generated by the elements of the form…
Hitting times provide a fundamental measure of distance in random processes, quantifying the expected number of steps for a random walk starting at node $u$ to reach node $v$. They have broad applications across domains such as network…
How fast a state of a system converges to a stationary state is one of the fundamental questions in science. Some Markov chains and random walks on finite groups are known to exhibit the non-asymptotic convergence to a stationary…
The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…
Social fragmentation transition is a transition of social states between many disconnected communities with distinct opinions and a well-connected single network with homogeneous opinions. This is a timely research topic with high relevance…
We consider Activated Random Walks on arbitrary finite networks, with particles being inserted at random and absorbed at the boundary. Despite the non-reversibility of the dynamics and the lack of knowledge on the stationary distribution,…
Many algorithms to detect communities in networks typically work without any information on the cluster structure to be found, as one has no a priori knowledge of it, in general. Not surprisingly, knowing some features of the unknown…
We examine the question of whether a collection of random walks on a graph can be coupled so that they never collide. In particular, we show that on the complete graph on n vertices, with or without loops, there is a Markovian coupling…
Spectral algorithms based on matrix representations of networks are often used to detect communities but classic spectral methods based on the adjacency matrix and its variants fail to detect communities in sparse networks. New spectral…
We present a novel approach to partitioning network nodes into non-overlapping communities - a key step in revealing network modularity and hierarchical organization. Our methodology, applicable to networks with both weighted and unweighted…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
We prove a large deviation principle for the sum of n independent heavy-tailed random variables, which are subject to a moving cut-off boundary at location n. Conditional on the sum being large at scale n, we show that a finite number of…
For a directed graph, the Pagerank algorithm emulates a random walker on the graph that occasionally "jumps" to a random vertex based on a jumping parameter $\alpha$. Upon completion, the algorithm generates a stochastic vector whose…
The random walk is fundamental to modeling dynamic processes on networks. Metrics based on the random walk have been used in many applications from image processing to Web page ranking. However, how appropriate are random walks to modeling…
In this paper, we consider networks consisting of a finite number of non-overlapping communities. To extract these communities, the interaction between pairs of nodes may be sampled from a large available data set, which allows a given node…
A sequence of graphs with diverging number of nodes is a dense graph sequence if the number of edges grows approximately as for complete graphs. To each such sequence a function, called graphon, can be associated, which contains information…
The Holme-Kim random graph processes is a variant of the Barabasi-Albert scale-free graph that was designed to exhibit clustering. In this paper we show that whether the model does indeed exhibit clustering depends on how we define the…
Many known networks have structure of affiliation networks, where each of $n$ network's nodes (actors) selects an attribute set from a given collection of $m$ attributes and two nodes (actors) establish adjacency relation whenever they…
New phase transition phenomena have recently been discovered for the stochastic block model, for the special case of two non-overlapping symmetric communities. This gives raise in particular to new algorithmic challenges driven by the…