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Motifs are the fundamental components of complex systems. The topological structure of networks representing complex systems and the frequency and distribution of motifs in these networks are intertwined. The complexities associated with…
There are extensive studies focusing on the application scenario that all the bipartite cohesive subgraphs need to be discovered in a bipartite graph. However, we observe that, for some applications, one is interested in finding bipartite…
We describe a synchronous distributed algorithm which identifies the edge-biconnected components of a connected network. It requires a leader, and uses messages of size O(log |V|). The main idea is to preorder a BFS spanning tree, and then…
Counting and finding triangles in graphs is often used in real-world analytics to characterize cohesiveness and identify communities in graphs. In this paper, we propose the novel concept of a cover-edge set that can be used to find…
The bipartite graph is a ubiquitous data structure that can model the relationship between two entity types: for instance, users and items, queries and webpages. In this paper, we study the problem of ranking vertices of a bipartite graph,…
Community Search (CS) aims to identify densely interconnected subgraphs corresponding to query vertices within a graph. However, existing heterogeneous graph-based community search methods need help identifying cross-group communities and…
We describe a technique for drawing values from discrete distributions, such as sampling from the random variables of a mixture model, that avoids computing a complete table of partial sums of the relative probabilities. A table of…
The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important…
A great variety of complex systems, from user interactions in communication networks to transactions in financial markets, can be modeled as temporal graphs consisting of a set of vertices and a series of timestamped and directed edges.…
Characterizing motif (i.e., locally connected subgraph patterns) statistics is important for understanding complex networks such as online social networks and communication networks. Previous work made the strong assumption that the graph…
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…
Dynamic networks, a.k.a. graph streams, consist of a set of vertices and a collection of timestamped interaction events (i.e., temporal edges) between vertices. Temporal motifs are defined as classes of (small) isomorphic induced subgraphs…
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…
The enumeration of minimal connected dominating sets is known to be notoriously hard for general graphs. Currently, it is only known that the sets can be enumerated slightly faster than $\mathcal{O}^{*}(2^n)$ and the algorithm is highly…
The eigenfunctions of the Laplacian are a natural basis of functions for many tasks in computational mathematics. On the circle and sphere, the eigenfunctions are given by complex periodic exponentials and spherical harmonics, respectively,…
We consider the fundamental problem of fairly allocating a set of indivisible items among agents having valuations that are represented by a multi-graph -- here, agents appear as vertices and items as edges between them and each vertex…
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…
Counting the number of small subgraphs, called motifs, is a fundamental problem in social network analysis and graph mining. Many real-world networks are directed and temporal, where edges have timestamps. Motif counting in directed,…
Networks are a fundamental tool for modeling complex systems in a variety of domains including social and communication networks as well as biology and neuroscience. Small subgraph patterns in networks, called network motifs, are crucial to…
We introduce Tiered Sampling, a novel technique for approximate counting sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size $M$, which…