Related papers: Heterogeneous Dense Subhypergraph Detection
We find an asymptotic enumeration formula for the number of simple $r$-uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations.…
This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and…
This paper studies detecting anomalous edges in directed graphs that model social networks. We exploit edge exchangeability as a criterion for distinguishing anomalous edges from normal edges. Then we present an anomaly detector based on…
There is a growing need for methods which can capture uncertainties and answer queries over graph-structured data. Two common types of uncertainty are uncertainty over the attribute values of nodes and uncertainty over the existence of…
Anomaly detection is a critical task in cybersecurity, where identifying insider threats, access violations, and coordinated attacks is essential for ensuring system resilience. Graph-based approaches have become increasingly important for…
In this paper, we consider an analog of the well-studied extremal problem for triangle-free subgraphs of graphs for uniform hypergraphs. A loose triangle is a hypergraph $T$ consisting of three edges $e,f$ and $g$ such that $|e \cap f| = |f…
Let $K_n$ be the complete graph with $n$ vertices and $c_1, c_2, ..., c_r$ be $r$ different colors. Suppose we randomly and uniformly color the edges of $K_n$ in $c_1, c_2, ..., c_r$. Then we get a random graph, denoted by…
This paper studies observability for non-uniform hypergraphs with inputs and outputs. To capture higher-order interactions, we define a canonical non-homogeneous dynamical system with nonlinear outputs on hypergraphs. We then construct…
A rough structure theorem is proved for graphs $G$ containing no copy of a bounded degree tree $T$: from any such $G$, one can delete $o(|G||T|)$ edges in order to get a subgraph all of whose connected components have a cover of order…
We consider classes of pseudo-random graphs on $n$ vertices for which the degree of every vertex and the co-degree between every pair of vertices are in the intervals $(np - Cn^\delta,np+Cn^\delta)$ and $(np^2- C n^\delta, np^2 +C…
The upper tail problem in a random graph asks to estimate the probability that the number of copies of some fixed subgraph in an Erd\H{o}s--R\'enyi random graph exceeds its expectation by some constant factor. There has been much exciting…
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…
While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the…
Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement…
Conventional network data has largely focused on pairwise interactions between two entities, yet multi-way interactions among multiple entities have been frequently observed in real-life hypergraph networks. In this article, we propose a…
The Lagrangian density of an $r$-uniform hypergraph $H$ is $r!$ multiplying the supremum of the Lagrangians of all $H$-free $r$-uniform hypergraphs. For an $r$-uniform graph $H$ with $t$ vertices, it is clear that $\pi_{\lambda}(H)\ge…
Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…
In this work, we consider hypothesis testing and anomaly detection on datasets where each observation is a weighted network. Examples of such data include brain connectivity networks from fMRI flow data, or word co-occurrence counts for…
We consider several detection situations where, under the alternative hypothesis, the signal admits a low complexity model and, under both the null and the alternative hypotheses, the distribution of the background noise is {unknown}. We…
Deep learning methods have proved highly effective for classification and image recognition problems. In this paper, we ask whether this success can be transferred to hypothesis testing: if a neural network can distinguish, for example, an…