Related papers: Testing Bipartitness in an Augmented VDF Bounded-D…
In property testing, a tester makes queries to (an oracle for) a graph and, on a graph having or being far from having a property P, it decides with high probability whether the graph satisfies P or not. Often, testers are restricted to a…
We propose a local-to-global strategy for graph machine learning and network analysis by defining certain local features and vector representations of nodes and then using them to learn globally defined metrics and properties of the nodes…
Given a graph $F$, the random Tur\'an problem asks to determine the maximum number of edges in an $F$-free subgraph of $G_{n,p}$. Prior to this work, the only bipartite graphs $F$ with known tight bounds included certain classes of complete…
In this paper, we study the cycle distribution of random low-density parity-check (LDPC) codes, randomly constructed protograph-based LDPC codes, and random quasi-cyclic (QC) LDPC codes. We prove that for a random bipartite graph, with a…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
Fraud detection on graph data can be viewed as a demanding task that requires distinguishing between different types of nodes. Because graph neural networks (GNNs) are naturally suited for processing information encoded in graph form…
A half-square of a bipartite graph $B=(X,Y,E_B)$ has one color class of $B$ as vertex set, say $X$; two vertices are adjacent whenever they have a common neighbor in $Y$. If $G=(V,E_G)$ is the half-square of a planar bipartite graph…
Measuring similarity between RDF graphs is essential for various applications, including knowledge discovery, semantic web analysis, and recommender systems. However, traditional similarity measures often treat all properties equally,…
We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…
We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be…
For a given $2$-partition $(V_1,V_2)$ of the vertices of a (di)graph $G$, we study properties of the spanning bipartite subdigraph $B_G(V_1,V_2)$ of $G$ induced by those arcs/edges that have one end in each $V_i$. We determine, for all…
Graph Generating Dependencies (GGDs) informally express constraints between two (possibly different) graph patterns which enforce relationships on both graph's data (via property value constraints) and its structure (via topological…
Given $n$-vertex simple graphs $X$ and $Y$, the friends-and-strangers graph $\mathsf{FS}(X, Y)$ has as its vertices all $n!$ bijections from $V(X)$ to $V(Y)$, where two bijections are adjacent if and only if they differ on two adjacent…
In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…
The problem of learning or reconstructing an unknown graph from a known family via partial-information queries arises as a mathematical model in various contexts. The most basic type of access to the graph is via \emph{edge queries}, where…
We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have…
In this paper we study the problem of testing graph isomorphism (GI) in the CONGEST distributed model. In this setting we test whether the distributive network, $G_U$, is isomorphic to $G_K$ which is given as an input to all the nodes in…
Randomness or mutual independence is a fundamental assumption forming the basis of statistical inference across disciplines such as economics, finance, and management. Consequently, validating this assumption is essential for the reliable…
We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and non-recurrent parts. We define the spectral complexity metric in terms of the…
When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…