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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, telecom-munication, 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… (More)

- Shankar Bhamidi, Remco Van Der Hofstad, Gerard Hooghiemstra
- 2009

We study first passage percolation on the configuration model. Assuming that each edge has an independent exponentially distributed edge weight, we derive explicit distributional asymptotics for the minimum weight between two randomly chosen connected vertices in the network, as well as for the number of edges on the least weight path, the so-called… (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)

- Shankar Bhamidi
- 2007

We study various properties of least cost paths under iid disorder for the complete graph and dense Erdos-Renyii random graphs in the connected phase, with iid exponential and uniform weights on edges. Using a simple heuristic, we compute explicitly, limiting distributions for (properly re-centered) lengths of shortest paths between typical nodes, as well… (More)

- Shankar Bhamidi, Remco Van Der Hofstad, Johan S H Van Leeuwaarden
- 2009

We find scaling limits for the sizes of the largest components at criticality for the rank-1 inho-mogeneous random graphs with power-law degrees with exponent τ. We investigate the case where τ ∈ (3, 4), so that the degrees have finite variance but infinite third moment. The sizes of the largest clusters, rescaled by n −(τ −2)/(τ −1) , converge to hitting… (More)

- Shankar Bhamidi, Remco Van Der Hofstad, Johan S H Van Leeuwaarden
- 2009

We identify the scaling limit for the sizes of the largest components at criticality for inhomoge-neous random graphs with weights that have finite third moments. We show that the sizes of the (rescaled) components converge to the excursion lengths of an inhomogeneous Brownian motion, which extends results of Aldous [1] for the critical behavior of Erd˝… (More)

- Shankar Bhamidi, Remco Van Der Hofstad, Gerard Hooghiemstra
- 2009

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)

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)

- Shankar Bhamidi
- 2007

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)

In this paper we explore first passage percolation (FPP) on the Erd˝ os-Rényi random graph G n (p n), where each edge is given an independent exponential edge weight with rate 1. In the sparse regime, i.e., when np n → λ > 1, we find refined asymptotics both for the minimal weight of the path between uniformly chosen vertices in the giant component, as well… (More)