Related papers: Optimal $(\alpha,\beta)$-Dense Subgraph Search in …
We describe a data structure that maintains the number of triangles in a dynamic undirected graph, subject to insertions and deletions of edges and of degree-zero vertices. More generally it can be used to maintain the number of copies of…
Bipartite graphs are ubiquitous in many domains, e.g., e-commerce platforms, social networks, and academia, by modeling interactions between distinct entity sets. Within these graphs, the butterfly motif, a complete 2*2 biclique, represents…
The problem of space-efficient depth-first search (DFS) is reconsidered. A particularly simple and fast algorithm is presented that, on a directed or undirected input graph $G=(V,E)$ with $n$ vertices and $m$ edges, carries out a DFS in…
Many common graph data mining tasks take the form of identifying dense subgraphs (e.g. clustering, clique-finding, etc). In biological applications, the natural model for these dense substructures is often a complete bipartite graph…
Subgraph queries also known as subgraph isomorphism search is a fundamental problem in querying graph-like structured data. It consists to enumerate the subgraphs of a data graph that match a query graph. This problem arises in many…
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.…
Mining maximal subgraphs with cohesive structures from a bipartite graph has been widely studied. One important cohesive structure on bipartite graphs is k-biplex, where each vertex on one side disconnects at most k vertices on the other…
Given a graph $G=(V, E)$ and and a proper labeling $f$ from $V$ to $\{1, ..., n\}$, we define $B(f)$ as the maximum absolute difference between $f(u)$ and $f(v)$ where $(u,v)\in E$. The bandwidth of $G$ is the minimum $B(f)$ for all $f$.…
Reachability query is a fundamental problem on graphs, which has been extensively studied in academia and industry. Since graphs are subject to frequent updates in many applications, it is essential to support efficient graph updates while…
Over the last decade, there has been an increasing interest in temporal graphs, pushed by a growing availability of temporally-annotated network data coming from social, biological and financial networks. Despite the importance of analyzing…
In a bipartite graph, a subgraph is an $s$-biplex if each vertex of the subgraph is adjacent to all but at most $s$ vertices on the opposite set. The enumeration of $s$-biplexes from a given graph is a fundamental problem in bipartite graph…
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…
The growing popularity of dynamic applications such as social networks provides a promising way to detect valuable information in real time. Efficient analysis over high-speed data from dynamic applications is of great significance. Data…
In many real-world applications such as social network analysis, knowledge graph discovery, biological network analytics, and so on, graph data management has become increasingly important and has drawn much attention from the database…
Embedding large graphs in low dimensional spaces has recently attracted significant interest due to its wide applications such as graph visualization, link prediction and node classification. Existing methods focus on computing the…
With an exponentially growing number of graphs from disparate repositories, there is a strong need to analyze a graph database containing an extensive collection of small- or medium-sized data graphs (e.g., chemical compounds). Although…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
There has been a rise in the popularity of algebraic methods for graph algorithms given the development of the GraphBLAS library and other sparse matrix methods. An exemplar for these approaches is Breadth-First Search (BFS). The algebraic…
With the prevalence of graphs for modeling complex relationships among objects, the topic of graph mining has attracted a great deal of attention from both academic and industrial communities in recent years. As one of the most fundamental…
This paper addresses the problem of finding the densest $k$-vertex subgraph in an arbitrary graph. This problem is NP-hard and has important applications in social network analysis, fraud detection, recommendation systems, and…