Related papers: Approximating Sparse Graphs: The Random Overlappin…
An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random…
It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of…
We propose the following model of a random graph on n vertices. Let F be a distribution in R_+^{n(n-1)/2} with a coordinate for every pair i$ with 1 \le i,j \le n. Then G_{F,p} is the distribution on graphs with n vertices obtained by…
For any graph consisting of $k$ vertices and $m$ edges we construct an ensemble of random pure quantum states which describe a system composed of $2m$ subsystems. Each edge of the graph represents a bi-partite, maximally entangled state.…
In this work we present a simple and efficient algorithm which, with high probability, provides an almost uniform sample from the set of proper k-colourings on an instance of a sparse random graph G(n,d/n), where k=k(d) is a sufficiently…
We study graphs that are formed by independently-positioned needles (i.e., line segments) in the unit square. To mathematically characterize the graph structure, we derive the probability that two line segments intersect and determine…
Let $d,n\in \mathbb{N}$ be such that $d=\omega(1)$, and $d\le n^{1-a}$ for some constant $a>0$. Consider a $d$-regular graph $G=(V, E)$ and the random graph process that starts with the empty graph $G(0)$ and at each step $G(i)$ is obtained…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…
In this paper, we present and analyze a simple and robust spectral algorithm for the stochastic block model with $k$ blocks, for any $k$ fixed. Our algorithm works with graphs having constant edge density, under an optimal condition on the…
We study ensembles of sparse random block matrices generated from the adjacency matrix of a Erd\"os-Renyi random graph with $N$ vertices of average degree $Z$, inserting a real symmetric $d \times d$ random block at each non-vanishing…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…
We study the expected adjacency matrix of a uniformly random multigraph with fixed degree sequence $\mathbf{d} \in \mathbb{Z}_+^n$. This matrix arises in a variety of analyses of networked data sets, including modularity-maximization and…
Dense subgraph discovery methods are routinely used in a variety of applications including the identification of a team of skilled individuals for collaboration from a social network. However, when the network's node set is associated with…
Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e. random graphs…
The approximate uniform sampling of graphs with a given degree sequence is a well-known, extensively studied problem in theoretical computer science and has significant applications, e.g., in the analysis of social networks. In this work we…
In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is closely connected to dense graph limits but its main…
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…