Related papers: Filtering Statistics on Networks
The online dominating set problem is an online variant of the minimum dominating set problem, which is one of the most important NP-hard problems on graphs. This problem is defined as follows: Given an undirected graph $G = (V, E)$, in…
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…
The increasing prevalence of graph-structured data across various domains has intensified greater interest in graph classification tasks. While numerous sophisticated graph learning methods have emerged, their complexity often hinders…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
We study mixing patterns in networks, meaning the propensity for nodes of different kinds to connect to one another. The phenomenon of assortative mixing, whereby nodes prefer to connect to others that are similar to themselves, has been…
A fundamental problem in signal processing is to denoise a signal. While there are many well-performing methods for denoising signals defined on regular supports, such as images defined on two-dimensional grids of pixels, many important…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
We consider the problem of enumerating all instances of a given pattern graph in a large data graph. Our focus is on determining the input/output (I/O) complexity of this problem. Let $E$ be the number of edges in the data graph, $k=O(1)$…
Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor…
The study of random graphs and networks had an explosive development in the last couple of decades. Meanwhile, techniques for the statistical analysis of sequences of networks were less developed. In this paper we focus on networks…
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…
The volume of data generated by internet and social networks is increasing every day, and there is a clear need for efficient ways of extracting useful information from them. As those data can take different forms, it is important to use…
We consider a dynamic model for competition in a social network, where two strategic agents have fixed beliefs and the non-strategic/regular agents adjust their states according to a distributed consensus protocol. We suppose that one…
To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
Graphs are extremely versatile and ubiquitous mathematical structures with potential to model a wide range of domains. For this reason, graph problems have been of interest since the early days of computer science. Some of these problems…
In this article we consider several probabilistic processes defining random grapha. One of these processes appeared recently in connection with a factorization problem in the symmetric group. For each of the probabilistic processes, we…
Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street…
Mapping the Internet generally consists in sampling the network from a limited set of sources by using "traceroute"-like probes. This methodology, akin to the merging of different spanning trees to a set of destinations, has been argued to…
We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…