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We calculate explicit formulae for the Shannon entropies of several families of tailored random graph ensembles for which no such formulae were as yet available, in leading orders in the system size. These include bipartite graph ensembles…
We obtain local weak limits in probability for Collapsed Branching Processes (CBP), which are directed random networks obtained by collapsing random-sized families of individuals in a general continuous-time branching process. The local…
Let $N$ local decision makers in a sensor network communicate with their neighbors to reach a decision \emph{consensus}. Communication is local, among neighboring sensors only, through noiseless or noisy links. We study the design of the…
We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…
Detecting communities in high-dimensional graphs can be achieved by applying random matrix theory where the adjacency matrix of the graph is modeled by a Stochastic Block Model (SBM). However, the SBM makes an unrealistic assumption that…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique…
Classical graphical modeling of multivariate random vectors uses graphs to encode conditional independence. In graphical modeling of multivariate stochastic processes, graphs may encode so-called local independence analogously. If some…
In this work we propose Lasagne, a methodology to learn locality and structure aware graph node embeddings in an unsupervised way. In particular, we show that the performance of existing random-walk based approaches depends strongly on the…
We study the undirected divisibility graph in which the vertex set is a finite subset of consecutive natural numbers up to N.We derive analytical expressions for measures of the graph like degree, clustering, geodesic distance and…
We present a sequential sampling methodology for weakly structural Markov laws, arising naturally in a Bayesian structure learning context for decomposable graphical models. As a key component of our suggested approach, we show that the…
Many community detection algorithms require the introduction of a measure on the set of nodes. Previously, a lot of efforts have been made to find the top-performing measures. In most cases, experiments were conducted on several datasets or…
Building upon the theory of graph limits and the Aldous-Hoover representation and inspired by Panchenko's work on asymptotic Gibbs measures (Annals of Probability 2013), we construct continuous embeddings of discrete probability…
A great deal of effort has been spent measuring topological features of the Internet. However, it was recently argued that sampling based on taking paths or traceroutes through the network from a small number of sources introduces a…
A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…
We investigate the distribution of eigenvalues of weighted adjacency matrices from a specific ensemble of random graphs. We distribute $N$ vertices across a fixed number $\kappa$ of components, with asymptotically $\alpha_j \dot N$ vertices…
Consider the setting of sparse graphs on N vertices, where the vertices have distinct "names", which are strings of length O(log N) from a fixed finite alphabet. For many natural probability models, the entropy grows as cN log N for some…
We propose a theoretical framework for training Graph Neural Networks (GNNs) on large input graphs via training on small, fixed-size sampled subgraphs. This framework is applicable to a wide range of models, including popular sampling-based…
Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or…