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Mining dense subgraphs is an important primitive across a spectrum of graph-mining tasks. In this work, we formally establish that two recurring characteristics of real-world graphs, namely heavy-tailed degree distributions and large…
The importance of classifying connections in large graphs has been the motivation for a rich line of work on distributed subgraph finding that has led to exciting recent breakthroughs. A crucial aspect that remained open was whether…
A locally irregular graph is a graph whose adjacent vertices have distinct degrees, a regular graph is a graph where each vertex has the same degree and a locally regular graph is a graph where for every two adjacent vertices u, v, their…
We consider mining dense substructures (maximal cliques) from an uncertain graph, which is a probability distribution on a set of deterministic graphs. For parameter 0 < {\alpha} < 1, we present a precise definition of an {\alpha}-maximal…
A key graph mining primitive is extracting dense structures from graphs, and this has led to interesting notions such as $k$-cores which subsequently have been employed as building blocks for capturing the structure of complex networks and…
Probabilistic circuits (PCs) represent a probability distribution as a computational graph. Enforcing structural properties on these graphs guarantees that several inference scenarios become tractable. Among these properties, structured…
Densest Subgraph Problem (DSP) is an important primitive problem with a wide range of applications, including fraud detection, community detection and DNA motif discovery. Edge-based density is one of the most common metrics in DSP.…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, informatics, and many other areas. Although there exist several algorithms with acceptable runtimes for certain classes of…
The concept of k-core, which indicates the largest induced subgraph where each node has k or more neighbors, plays a significant role in measuring the cohesiveness and the engagement of a network, and it is exploited in diverse…
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…
How can we find a good graph clustering of a real-world network, that allows insight into its underlying structure and also potential functions? In this paper, we introduce a new graph clustering algorithm Dcut from a density point of view.…
Dense subgraph discovery methods are routinely used in a variety of applications including the identification of a team of skilled individuals for collaboration from a social network. However, when the network's node set is associated with…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
Finding the densest subgraph (DS) from a graph is a fundamental problem in graph databases. The DS obtained, which reveals closely related entities, has been found to be useful in various application domains such as e-commerce, social…
Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…
We study the NP-hard graph problem Collapsed k-Core where, given an undirected graph G and integers b, x, and k, we are asked to remove b vertices such that the k-core of remaining graph, that is, the (uniquely determined) largest induced…
We study the problem of clustering nodes in a dynamic graph, where the connections between nodes and nodes' cluster memberships may change over time, e.g., due to community migration. We first propose a dynamic stochastic block model that…
Tackling molecular optimization problems using conventional computational methods is challenging, because the determination of the optimized configuration is known to be an NP-hard problem. Recently, there has been increasing interest in…
The $k$-truss, introduced by Cohen (2005), is a graph where every edge is incident to at least $k$ triangles. This is a relaxation of the clique. It has proved to be a useful tool in identifying cohesive subnetworks in a variety of…
Let $\mathcal{D}$ be a set of straight-line segments in the plane, potentially crossing, and let $c$ be a positive integer. We denote by $P$ the union of the endpoints of the straight-line segments of $\mathcal{D}$ and of the intersection…