Related papers: Distance distribution in random graphs and applica…
Measuring the distances between vertices on graphs is one of the most fundamental components in network analysis. Since finding shortest paths requires traversing the graph, it is challenging to obtain distance information on large graphs…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
We consider a statistical model for the problem of finding subgraphs with specified topology in an otherwise random graph. This task plays an important role in the analysis of social and biological networks. In these types of networks,…
We consider the problem of searching for a node on a labelled random graph according to a greedy algorithm that selects a route to the desired node using metric information on the graph. Motivated by peer-to-peer networks two types of…
A great deal of effort has been spent measuring topological features of the Internet. However, it was recently argued that sampling based on taking paths or traceroutes through the network from a small number of sources introduces a…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…
In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
Finding important edges in a graph is a crucial problem for various research fields, such as network epidemics, signal processing, machine learning, and sensor networks. In this paper, we tackle the problem based on sampling theory on…
Hypergraphs, graph generalizations where edges are conglomerates of $r$ nodes called hyperedges of rank $r\geq 2$, are excellent models to study systems with interactions that are beyond the pairwise level. For hypergraphs, the node degree…
A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is…
Given two subsets A and B of nodes in a directed graph, the conduciveness of the graph from A to B is the ratio representing how many of the edges outgoing from nodes in A are incoming to nodes in B. When the graph's nodes stand for the…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, $N$. In this paper, we present a novel derivation of the…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Consider the continuum of points along the edges of a network, i.e., an undirected graph with positive edge weights. We measure distance between these points in terms of the shortest path distance along the network, known as the network…
Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…
Probabilistic graphs are an abstraction that allow us to study randomized propagation in graphs. In a probabilistic graph, each edge is "active" with a certain probability, independent of the other edges. For two vertices $u,v$, a classic…
We consider a latent space model for random graphs where a node $i$ is associated to a random latent point $X_i$ on the Euclidean unit ball. The probability that an edge exists between two nodes is determined by a ``link'' function, which…