Shankar Bhamidi

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A variety of random graph models have been developed in recent years to study a range of problems on networks, driven by the wide availability of data from many social, telecommunication, biochemical and other networks. A key model, extensively used in the sociology literature, is the exponential random graph model. This model seeks to incorporate in random(More)
<lb>We study first passage percolation on the configuration model. Assuming that each edge has an<lb>independent exponentially distributed edge weight, we derive explicit distributional asymptotics for<lb>the minimum weight between two randomly chosen connected vertices in the network, as well as for<lb>the number of edges on the least weight path, the(More)
In this paper we explore first passage percolation (FPP) on the Erdős-Rényi random graph Gn(pn), where each edge is given an independent exponential edge weight with rate 1. In the sparse regime, i.e., when npn → λ > 1, we find refined asymptotics both for the minimal weight of the path between uniformly chosen vertices in the giant component, as well as(More)
We use embeddings in continuous time Branching processes to derive asymptotics for various statistics associated with different models of preferential attachment. This powerful method allows us to deduce, with very little effort, under a common framework, not only local characteristics for a wide class of scale free trees, but also global characteristics(More)
We demonstrate the use of computational phylogenetic techniques to solve a central problem in inferential network monitoring. More precisely, we design a novel algorithm for multicast-based delay inference, i.e. the problem of reconstructing the topology and delay characteristics of a network from end-to-end delay measurements on network paths. Our(More)
We analyze the eigenvalues of the adjacency matrices of a wide variety of random trees. Using general, broadly applicable arguments based on the interlacing inequalities for the eigenvalues of a principal submatrix of a Hermitian matrix and a suitable notion of local weak convergence for an ensemble of random trees that we call probability fringe(More)
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a uniform X logX-condition, we analyze the asymptotic distribution for the minimal weight path between a pair of typical(More)
Motivated by “condensation” phenomena often observed in social networks such as Twitter where one “superstar” vertex gains a positive fraction of the edges, while the remaining empirical degree distribution still exhibits a power law tail, we formulate a mathematically tractable model for this phenomenon which provides a better fit to empirical data than(More)
We study first passage percolation on the configuration model (CM) having power-law degrees with exponent τ ∈ [1, 2). To this end, we equip the edges with exponential weights. We derive the distributional limit of the minimal weight of a path between typical vertices in the network and the number of edges on the minimal weight path, which can be computed in(More)