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We present a method that allows for the discovery of communities within graphs of arbitrary size in times that scale linearly with their size. This method avoids edge cutting and is based on notions of voltage drops across networks that are…
With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…
For distributed graph processing on massive graphs, a graph is partitioned into multiple equally-sized parts which are distributed among machines in a compute cluster. In the last decade, many partitioning algorithms have been developed…
The process of drawing electoral district boundaries is known as political redistricting. Within this context, gerrymandering is the practice of drawing these boundaries such that they unfairly favor a particular political party, often…
We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes. Our methods are based on the computation of extremal eigenvalues of the…
Analyzing large graph data is an essential part of many modern applications, such as social networks. Due to its large computational complexity, distributed processing is frequently employed. This requires graph data to be divided across…
In this paper, we show reduction methods for search algorithms on graphs using quantum walks. By using a graph partitioning method called equitable partition for the the given graph, we determine "effective subspace" for the search…
Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…
In this paper we study the problem of discovering a timeline of events in a temporal network. We model events as dense subgraphs that occur within intervals of network activity. We formulate the event-discovery task as an optimization…
For random walks on graph $\mathcal{G}$ with $n$ vertices and $m$ edges, the mean hitting time $H_j$ from a vertex chosen from the stationary distribution to vertex $j$ measures the importance for $j$, while the Kemeny constant…
We give faster algorithms for producing sparse approximations of the transition matrices of $k$-step random walks on undirected, weighted graphs. These transition matrices also form graphs, and arise as intermediate objects in a variety of…
The theory of rapid mixing random walks plays a fundamental role in the study of modern randomised algorithms. Usually, the mixing time is measured with respect to the worst initial position. It is well known that the presence of…
We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…
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…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
Given a time-evolving network, how can we detect communities over periods of high internal and low external interactions? To address this question we generalize traditional local community detection in graphs to the setting of dynamic…
Let $H$ be a fixed undirected graph on $k$ vertices. The $H$-hitting set problem asks for deleting a minimum number of vertices from a given graph $G$ in such a way that the resulting graph has no copies of $H$ as a subgraph. This problem…
Image segmentation has many applications which range from machine learning to medical diagnosis. In this paper, we propose a framework for the segmentation of images based on super-pixels and algorithms for community identification in…
Graph clustering or community detection constitutes an important task for investigating the internal structure of graphs, with a plethora of applications in several domains. Traditional techniques for graph clustering, such as spectral…
Community detection refers to finding densely connected groups of nodes in graphs. In important applications, such as cluster analysis and network modelling, the graph is sparse but outliers and heavy-tailed noise may obscure its structure.…