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Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network…
Graph matching is the process of computing the similarity between two graphs. Depending on the requirement, it can be exact or inexact. Exact graph matching requires a strict correspondence between nodes of two graphs, whereas inexact…
We present a novel graph embedding space (i.e., a set of measures on graphs) for performing statistical analyses of networks. Key improvements over existing approaches include discovery of "motif-hubs" (multiple overlapping significant…
A new heuristic based on vertex invariants is developed to rapidly distinguish non-isomorphic graphs to a desired level of accuracy. The method is applied to sample subgraphs from an E.coli protein interaction network, and as a probe for…
Mining dense quasi-cliques is a well-known clustering task with applications ranging from social networks over collaboration graphs to document analysis. Recent work has extended this task to multiple graphs; i.e. the goal is to find groups…
Social media data are often modeled as heterogeneous graphs with multiple types of nodes and edges. We present a discovery algorithm that first chooses a "background" graph based on a user's analytical interest and then automatically…
The Subgraph Matching (SM) problem consists of finding all the embeddings of a given small graph, called the query, into a large graph, called the target. The SM problem has been widely studied for simple graphs, i.e. graphs where there is…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
Subgraph recognition aims at discovering a compressed substructure of a graph that is most informative to the graph property. It can be formulated by optimizing Graph Information Bottleneck (GIB) with a mutual information estimator.…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
The subgraph enumeration problem asks us to find all subgraphs of a target graph that are isomorphic to a given pattern graph. Determining whether even one such isomorphic subgraph exists is NP-complete---and therefore finding all such…
We give the first fully dynamic algorithm which maintains a $(1-\epsilon)$-approximate densest subgraph in worst-case time $\text{poly}(\log n, \epsilon^{-1})$ per update. Dense subgraph discovery is an important primitive for many…
Social media data are often modeled as heterogeneous graphs with multiple types of nodes and edges. We present a discovery algorithm that first chooses a "background" graph based on a user's analytical interest and then automatically…
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…
Dense subgraph discovery is an important graph-mining primitive with a variety of real-world applications. One of the most well-studied optimization problems for dense subgraph discovery is the densest subgraph problem, where given an…
Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, joint interactions of proteins, to name a few. In this work, we propose tools for answering the…
Consider the following stochastic matching problem. Given a graph $G=(V, E)$, an unknown subgraph $G_p = (V, E_p)$ is realized where $E_p$ includes every edge of $E$ independently with some probability $p \in (0, 1]$. The goal is to query a…
For the past decades, the \textit{subgraph similarity search} over a large-scale data graph has become increasingly important and crucial in many real-world applications, such as social network analysis, bioinformatics network analytics,…
Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasi-cliques from a graph is a robust way to detect densely connected structures with applications to bio-informatics and social…
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…