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Estimating similarity between vertices is a fundamental issue in network analysis across various domains, such as social networks and biological networks. Methods based on common neighbors and structural contexts have received much…
In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…
We give a deterministic algorithm for computing a global minimum vertex cut in a vertex-weighted graph $n$ vertices and $m$ edges in $\widehat O(mn)$ time. This breaks the long-standing $\widehat \Omega(n^{4})$-time barrier in dense graphs,…
For a class $\mathcal{H}$ of graphs, #Sub$(\mathcal{H})$ is the counting problem that, given a graph $H\in \mathcal{H}$ and an arbitrary graph $G$, asks for the number of subgraphs of $G$ isomorphic to $H$. It is known that if $\mathcal{H}$…
A popular way to define or characterize graph classes is via forbidden subgraphs or forbidden minors. These characterizations play a key role in graph theory, but they rarely lead to efficient algorithms to recognize these classes. In…
Context: The growing size of graph-based modeling artifacts in model-driven engineering calls for techniques that enable efficient execution of graph queries. Incremental approaches based on the RETE algorithm provide an adequate solution…
A graph embedding algorithm embeds a graph into a low-dimensional space such that the embedding preserves the inherent properties of the graph. While graph embedding is fundamentally related to graph visualization, prior work did not…
We study the problem of finding and monitoring fixed-size subgraphs in a continually changing large-scale graph. We present the first approach that (i) performs worst-case optimal computation and communication, (ii) maintains a total memory…
Subgraph counting aims to count the occurrences of a subgraph template T in a given network G. The basic problem of computing structural properties such as counting triangles and other subgraphs has found applications in diverse domains.…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
A new efficient algorithm is presented for finding all simple cycles that satisfy a length constraint in a directed graph. When the number of vertices is non-trivial, most cycle-finding problems are of practical interest for sparse graphs…
In 1985, Chv\'{a}tal introduced the concept of star cutsets as a means to investigate the properties of perfect graphs, which inspired many researchers to study cutsets with some specific structures, for example, star cutsets, clique…
We describe algorithms to efficiently compute minimum $(s,t)$-cuts and global minimum cuts of undirected surface-embedded graphs. Given an edge-weighted undirected graph $G$ with $n$ vertices embedded on an orientable surface of genus $g$,…
The rise of graph analytic systems has created a need for ways to measure and compare the capabilities of these systems. Graph analytics present unique scalability difficulties. The machine learning, high performance computing, and visual…
Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…
Graphs have been widely used in many applications such as social networks, collaboration networks, and biological networks. One important graph analytics is to explore cohesive subgraphs in a large graph. Among several cohesive subgraphs…
Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…
In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…
Dense subgraph extraction is a fundamental problem in graph analysis and data mining, aimed at identifying cohesive and densely connected substructures within a given graph. It plays a crucial role in various domains, including social…
In this paper we show how to efficiently produce unbiased estimates of subgraph frequencies from a probability sample of egocentric networks (i.e., focal nodes, their neighbors, and the induced subgraphs of ties among their neighbors). A…