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The expressivity of Graph Neural Networks (GNNs) is dependent on the aggregation functions they employ. Theoretical works have pointed towards Sum aggregation GNNs subsuming every other GNNs, while certain practical works have observed a…
We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…
Directed graphs are widely used to model data flow and execution dependencies in streaming applications. This enables the utilization of graph partitioning algorithms for the problem of parallelizing computation for multiprocessor…
The problem of computing sum of sources over a multiple access channel (MAC) is considered. Building on the technique of linear computation coding (LCC) proposed by Nazer and Gastpar [2007], we employ the ensemble of nested coset codes to…
Directed acyclic graphs provide a fundamental tool for representing directed dependence structures in multivariate network data, and are widely used to model financial and economic networks. However, accurate and interpretable estimation…
We consider the multiple unicast problem with three source-terminal pairs over directed acyclic networks with unit-capacity edges. The three $s_i-t_i$ pairs wish to communicate at unit-rate via network coding. The connectivity between the…
In this paper, we investigate the problem of generating the spanning trees of a graph $G$ up to the automorphisms or "symmetries" of $G$. After introducing and surveying this problem for general input graphs, we present algorithms that…
We address the problem of constructing large undirected circulant networks with given degree and diameter. First we discuss the theoretical upper bounds and their asymptotics, and then we describe and implement a computer-based method to…
We study the limits of communication efficiency for function computation in collocated networks within the framework of multi-terminal block source coding theory. With the goal of computing a desired function of sources at a sink, nodes…
A sum-product network (SPN) is a probabilistic model, based on a rooted acyclic directed graph, in which terminal nodes represent univariate probability distributions and non-terminal nodes represent convex combinations (weighted sums) and…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
The capacity of a channel characterizes the maximum rate at which information can be transmitted through the channel asymptotically faithfully. For a channel with multiple senders and a single receiver, computing its sum capacity is…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
The entropy of a digraph is a fundamental measure which relates network coding, information theory, and fixed points of finite dynamical systems. In this paper, we focus on the entropy of undirected graphs. We prove that for any integer $k$…
We consider the problem of information aggregation in sensor networks, where one is interested in computing a function of the sensor measurements. We allow for block processing and study in-network function computation in directed graphs…
Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…
While feasibility and obtaining a solution of a given network coding problem are well studied, the decoding procedure and complexity have not garnered much attention. We consider the decoding problem in a network wherein the sources…
We study a network utility maximization (NUM) decomposition in which the set of flow rates is grouped by source-destination pairs. We develop theorems for both single-path and multipath cases, which relate an arbitrary NUM problem involving…
We study synchronization and consensus in a group of dynamical systems coupled via multiple directed networks. We show that even though the coupling in a single network may not be sufficient to synchronize the systems, combination of…