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Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…
Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition…
A hypergraph ${\cal F}$ is a set family defined on vertex set $V$. The dual of ${\cal F}$ is the set of minimal subsets $H$ of $V$ such that $F\cap H \ne \emptyset$ for any $F\in {\cal F}$. The computation of the dual is equivalent to many…
Subgraph matching is a core task in graph analytics, widely used in domains such as biology, finance, and social networks. Existing top-k diversified methods typically focus on maximizing vertex coverage, but often return results in the…
The $k$-defective clique model relaxes the strict completeness constraint of the traditional clique by allowing up to $k$ missing edges, providing a robust formulation for detecting cohesive structures in noisy graphs. Consequently, the…
Given query access to an undirected graph $G$, we consider the problem of computing a $(1\pm\epsilon)$-approximation of the number of $k$-cliques in $G$. The standard query model for general graphs allows for degree queries, neighbor…
Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix…
In this note, we investigate listing cliques of arbitrary sizes in bandwidth-limited, dynamic networks. The problem of detecting and listing triangles and cliques was originally studied in great detail by Bonne and Censor-Hillel (ICALP…
(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…
Important graph mining problems such as Clustering are computationally demanding. To significantly accelerate these problems, we propose ProbGraph: a graph representation that enables simple and fast approximate parallel graph mining with…
Bipartite graphs are a prevalent modeling tool for real-world networks, capturing interactions between vertices of two different types. Within this framework, bicliques emerge as crucial structures when studying dense subgraphs: they are…
Dense linear algebra kernels are critical for wireless applications, and the oncoming proliferation of 5G only amplifies their importance. Many such matrix algorithms are inductive, and exhibit ample amounts of fine-grain ordered…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
Big graphs (networks) arising in numerous application areas pose significant challenges for graph analysts as these graphs grow to billions of nodes and edges and are prohibitively large to fit in the main memory. Finding the number of…
Freehand sketches exhibit unique sparsity and abstraction, necessitating learning pipelines distinct from those designed for images. For sketch learning methods, the central objective is to fully exploit the effective information embedded…
The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k are removed until there are no vertices of degree less than k left. The remaining hypergraph…
The problem of identifying the maximum edge biclique in bipartite graphs has attracted considerable attention in bipartite graph analysis, with numerous real-world applications such as fraud detection, community detection, and online…
A graph is $k$-clique-extendible if there is an ordering of the vertices such that whenever two $k$-sized overlapping cliques $A$ and $B$ have $k-1$ common vertices, and these common vertices appear between the two vertices $a,b\in…
Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…