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Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…
The minimum $s$-$t$ cut problem in graphs is one of the most fundamental problems in combinatorial optimization, and graph cuts underlie algorithms throughout discrete mathematics, theoretical computer science, operations research, and data…
Dense subgraph discovery aims to find a dense component in edge-weighted graphs. This is a fundamental graph-mining task with a variety of applications and thus has received much attention recently. Although most existing methods assume…
The graph partitioning problem has many applications in scientific computing such as computer aided design, data mining, image compression and other applications with sparse-matrix vector multiplications as a kernel operation. In many cases…
For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…
We develop a matrix approach to the Maximal Acyclic Subgraph (MAS) problem by reducing it to finding the closest nilpotent matrix to the matrix of the graph. Using recent results on the closest Schur stable systems and on minimising the…
In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently…
A central problem in graph mining is finding dense subgraphs, with several applications in different fields, a notable example being identifying communities. While a lot of effort has been put on the problem of finding a single dense…
The densest $k$-subgraph problem is the problem of finding a $k$-vertex subgraph of a graph with the maximum number of edges. In order to solve large instances of the densest $k$-subgraph problem, we introduce two algorithms that are based…
The problem of finding dense components of a graph is a widely explored area in data analysis, with diverse applications in fields and branches of study including community mining, spam detection, computer security and bioinformatics. This…
Dirac proved that each $n$-vertex $2$-connected graph with minimum degree at least $k$ contains a cycle of length at least $\min\{2k, n\}$. We consider a hypergraph version of this result. A Berge cycle in a hypergraph is an alternating…
Detecting a small number of outliers from a set of data observations is always challenging. This problem is more difficult in the setting of multiple network samples, where computing the anomalous degree of a network sample is generally not…
The weight of the minimum spanning tree in a complete weighted graph with random edge weights is a well-known problem. For various classes of distributions, it is proved that the weight of the minimum spanning tree tends to a constant,…
Subgraph counting aims to count occurrences of a template T in a given network G(V, E). It is a powerful graph analysis tool and has found real-world applications in diverse domains. Scaling subgraph counting problems is known to be memory…
Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…
We study a number of graph exploration problems in the following natural scenario: an algorithm starts exploring an undirected graph from some seed node; the algorithm, for an arbitrary node $v$ that it is aware of, can ask an oracle to…
In this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of…
We study subgraph counting over fully dynamic graphs, which undergo edge insertions and deletions. Counting subgraphs is a fundamental problem in graph theory with numerous applications across various fields, including database theory,…
The bloom of complex network study, in particular, with respect to scale-free ones, is considerably triggering the research of scale-free graph itself. Therefore, a great number of interesting results have been reported in the past,…
We address a specific case of the matroid intersection problem: given a set of graphs sharing the same set of vertices, select a minimum cycle basis for each graph to maximize the size of their intersection. We provide a comprehensive…