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Network comparison is a widely-used tool for analyzing complex systems, with applications in varied domains including comparison of protein interactions or highlighting changes in structure of trade networks. In recent years, a number of…
Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
This paper deals with a universal coding problem for a certain kind of multiterminal source coding network called a generalized complementary delivery network. In this network, messages from multiple correlated sources are jointly encoded,…
The following \textit{network computing} problem is considered. Source nodes in a directed acyclic network generate independent messages and a single receiver node computes a target function $f$ of the messages. The objective is to maximize…
In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to…
We propose an algorithm for average consensus over a directed graph which is both fully asynchronous and robust to unreliable communications. We show its convergence to the average, while allowing for slowly growing but potentially…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
Last mile link is often a bottleneck for end user. However, users typically have multiple ways of accessing the Internet (cellular, ADSL, public Wifi). This observation led to creation of protocols like mTCP or R-MTP. Current bandwidth…
From any given sequence of finite or infinite graphs, a nonstandard graph is constructed. The procedure is similar to an ultrapower construction of an internal set from a sequence of subsets of the real line, but now the individual entities…
In this paper, we use the linear deterministic approximation model to study a two user multiple access channel mutually interfering with a point to point link, which represents a basic setup of a cellular system. We derive outer bounds on…
The structure of many financial networks is protected by privacy and has to be inferred from aggregate observables. Here we consider one of the most successful network reconstruction methods, producing random graphs with desired link…
Online social networks are a dominant medium in everyday life to stay in contact with friends and to share information. In Twitter, users can connect with other users by following them, who in turn can follow back. In recent years,…
We consider a communication network with a single source that has a set of messages and two terminals where each terminal is interested in an arbitrary subset of messages at the source. A tight capacity region for this problem is…
In this paper, we investigate the problem of recovering source information from an incomplete set of network coded data. We first study the theoretical performance of such systems under maximum a posteriori (MAP) decoding and derive the…
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
We consider that a network is an observation, and a collection of observed networks forms a sample. In this setting, we provide methods to test whether all observations in a network sample are drawn from a specified model. We achieve this…
In this paper we describe a generic scheme for the parallel exploration of directed acyclic graphs starting from one or more `roots' of the graph. Our scheme is designed for graphs with the following properties, (i) discovering neighbors at…