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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)
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)
The percolation phase transition and the mechanism of the emergence of the giant component through the critical scaling window for random graph models, has been a topic of great interest in many different communities ranging from statistical physics, combinatorics, computer science, social networks and probability theory. The last few years have witnessed(More)
A common and important problem arising in the study of networks is how to divide the vertices of a given network into one or more groups, called communities, in such a way that vertices of the same community are more interconnected than vertices belonging to different ones. We propose and investigate a testing based community detection procedure called(More)
Partitioning a network into different communities so that vertices of the same community share meaningful density-and pattern-based similarities is an important area of research in the field of network science. For directed networks identifying communities turns out to be especially challenging since the directed nature of the edges makes it difficult to(More)
Consider the complete n-vertex graph whose edge-lengths are independent exponentially distributed random variables. Simultaneously for each pair of vertices, put a constant flow between them along the shortest path. Each edge gets some random total flow. In the n → ∞ limit we find explicitly the empirical distribution of these edge-flows, suitably(More)
BACKGROUND Peer relationships are important for children's mental health, yet little is known of their etiological underpinnings. Here, we explore the genetic influences on childhood peer network characteristics in three different networks defined by rejection, acceptance, and prosocial behavior. We further examine the impact of early externalizing and(More)
Community detection is the process of grouping strongly connected nodes in a network. Many community detection methods for un-weighted networks have a theoretical basis in a null model, which provides an interpretation of resulting communities in terms of statistical significance. In this paper, we introduce a null for sparse weighted networks called the(More)
In this paper we explore maximal deviations of large random structures from their typical behavior. We introduce a model for a high-dimensional random graph process and ask analogous questions to those of Vapnik and Chervonenkis for deviations of averages: how " rich " does the process have to be so that one sees atypical behavior. In particular, we study a(More)