Related papers: On Connectivity and Robustness in Random Intersect…
Random key graphs have received considerable attention and been used in various applications including secure sensor networks, social networks, the study of epidemics, cryptanalysis, and recommender systems. In this paper, we investigate a…
Uniform random intersection graphs have received much interest and been used in diverse applications. A uniform random intersection graph with $n$ nodes is constructed as follows: each node selects a set of $K_n$ different items uniformly…
Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbours to each point of a dataset to perform their tasks. These proximity relations define a so-called…
Network robustness is an essential system property to sustain functionality in the face of failures or targeted attacks. Currently, only the connectivity of the nodes unaffected by an attack is utilized to assess robustness. We propose to…
Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to…
Since their introduction by Kipf and Welling in $2017$, a primary use of graph convolutional networks is transductive node classification, where missing labels are inferred within a single observed graph and its feature matrix. Despite the…
A unified approach to studying convergence and stochastic stability of continuous time consensus protocols (CPs) is presented in this work. Our method applies to networks with directed information flow; both cooperative and noncooperative…
Let $G_1,\dots, G_m$ be independent identically distributed Bernoulli random subgraphs of the complete graph ${\cal K}_n$ having vertex sets of random sizes $X_1,\dots, X_m\in \{0,1,2,\dots\}$ and random edge densities $Q_1,\dots, Q_m\in…
A graph is called $d$-rigid if there exists a generic embedding of its vertex set into $\mathbb{R}^d$ such that every continuous motion of the vertices that preserves the lengths of all edges actually preserves the distances between all…
We will present a new method, which enables us to find threshold functions for many properties in random intersection graphs. This method will be used to establish sharp threshold functions in random intersection graphs for k-connectivity,…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
An intuitive property of a random graph is that its subgraphs should also appear randomly distributed. We consider graphs whose subgraph densities exactly match their expected values. We call graphs with this property for all subgraphs with…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
Quasi-random graphs can be informally described as graphs whose edge distribution closely resembles that of a truly random graph of the same edge density. Recently, Shapira and Yuster proved the following result on quasi-randomness of…
Many works show that node-level predictions of Graph Neural Networks (GNNs) are unrobust to small, often termed adversarial, changes to the graph structure. However, because manual inspection of a graph is difficult, it is unclear if the…
Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
K-cores are maximal induced subgraphs where all vertices have degree at least k. These dense patterns have applications in community detection, network visualization and protein function prediction. However, k-cores can be quite unstable to…
The k-core of a graph G is the maximal subgraph of G having minimum degree at least k. In 1996, Pittel, Spencer and Wormald found the threshold $\lambda_c$ for the emergence of a non-trivial k-core in the random graph $G(n,\lambda/n)$, and…
The apparent disconnection between the microscopic and the macroscopic is a major issue in the understanding of complex systems. To this extend, we study the convergence of repeatedly applying local rules on a network, and touch on the…
This paper investigates the addition of random edges to arbitrary dense graphs; in particular, we determine the number of random edges required to ensure various monotone properties including the appearance of a fixed size clique, small…