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Let $\{D_M\}_{M\geq 0}$ be the $n$-vertex random directed graph process, where $D_0$ is the empty directed graph on $n$ vertices, and subsequent directed graphs in the sequence are obtained by the addition of a new directed edge uniformly…
Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level graphs, that is, graphs obtained from an edge-weighted graph by removing all sufficiently light…
Graph machine learning has been extensively studied in both academia and industry. Although booming with a vast number of emerging methods and techniques, most of the literature is built on the in-distribution hypothesis, i.e., testing and…
Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a…
We give characterizations of the structure and degree sequences of hereditary unigraphs, those graphs for which every induced subgraph is the unique realization of its degree sequence. The class of hereditary unigraphs properly contains the…
We define dual-critical graphs as graphs having an acyclic orientation, where the indegrees are odd except for the unique source. We have very limited knowledge about the complexity of dual-criticality testing. By the definition the problem…
A directed multigraph is said vulnerable if it can generate Braess paradox in Traffic Networks. In this paper, we give a graph-theoretic characterisation of vulnerable directed multigraphs; analogous results appeared in the literature only…
A graph property is said to be elusive ( evasive) if every algorithm testing this property by asking questions of the form "is there an edge between vertices x and y" requires, in the worst case, to ask about all pairs of vertices. The…
Symmetric independence relations are often studied using graphical representations. Ancestral graphs or acyclic directed mixed graphs with $m$-separation provide classes of symmetric graphical independence models that are closed under…
The Graph Reconstruction Conjecture famously posits that any undirected graph on at least three vertices is determined up to isomorphism by its family of (unlabeled) induced subgraphs. At present, the conjecture admits partial resolutions…
This paper contains two finite-sample results concerning the sign test. First, we show that the sign-test is unbiased with independent, non-identically distributed data for both one-sided and two-sided hypotheses. The proof for the…
Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…
A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…
Degree-based graph construction is an ubiquitous problem in network modeling, ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive…
We show that the graph property of having a (very) large $k$-th Betti number $\beta_k$ for constant $k$ is testable with a constant number of queries in the dense graph model. More specifically, we consider a clique complex defined by an…
We study different geometric properties on infinite graphs, related to the weak-type boundedness of the Hardy-Littlewood maximal averaging operator. In particular, we analyze the connections between the doubling condition, having finite…
We determine if the width of a graph class ${\cal G}$ changes from unbounded to bounded if we consider only those graphs from ${\cal G}$ whose diameter is bounded. As parameters we consider treedepth, pathwidth, treewidth and clique-width,…
Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, and visual understanding. Generating such graphs enables tasks such as simulation, data…
Graph Neural Networks (GNNs) have achieved remarkable success in various applications, but their performance can be sensitive to specific data properties of the graph datasets they operate on. Current literature on understanding the…