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As networks continue to increase in size, current methods must be capable of handling large numbers of nodes and edges in order to be practically relevant. Instead of working directly with the entire (large) network, analyzing sub-networks…
Graph is an important data representation which occurs naturally in the real world applications \cite{goyal2018graph}. Therefore, analyzing graphs provides users with better insights in different areas such as anomaly detection…
In the k-arc connected subgraph problem, we are given a directed graph G and an integer k and the goal is the find a subgraph of minimum cost such that there are at least k-arc disjoint paths between any pair of vertices. We give a simple…
The discovery of the "hidden population", whose size and membership are unknown, is made possible by assuming that its members are connected in a social network by their relationships. We explore these groups by a chain-referral sampling…
Social tagging, as a novel approach to information organization and discovery, has been widely adopted in many Web2.0 applications. The tags provide a new type of information that can be exploited by recommender systems. Nevertheless, the…
Public-private graph, where a public network is visible to everyone and every user is also associated with its own small private graph accessed by itself only, widely exists in real-world applications of social networks and financial…
We consider the problem of a Parameter Server (PS) that wishes to learn a model that fits data distributed on the nodes of a graph. We focus on Federated Learning (FL) as a canonical application. One of the main challenges of FL is the…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
Bipartite graphs are widely used to model relationships between two types of entities. Community search retrieves densely connected subgraphs containing a query vertex, which has been extensively studied on unipartite graphs. However,…
The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central…
Community structure is one of the most important properties of networks. Most community algorithms are not suitable for large networks because of their time consuming. In fact there are lots of networks with millons even billons of nodes.…
In a recent work by Novo et al. (Sci. Rep. 5, 13304, 2015), the invariant subspace method was applied to the study of continuous-time quantum walk (CTQW). The method helps to reduce a graph into a simpler version that allows more…
We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let…
A $k$-clique is a dense graph, consisting of $k$ fully-connected nodes, that finds numerous applications, such as community detection and network analysis. In this paper, we study a new problem, that finds a maximum set of disjoint…
Community analysis algorithm proposed by Clauset, Newman, and Moore (CNM algorithm) finds community structure in social networks. Unfortunately, CNM algorithm does not scale well and its use is practically limited to networks whose sizes…
Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between…
A novel approach rooted on the notion of consensus clustering, a strategy developed for community detection in complex networks, is proposed to cope with the heterogeneity that characterizes connectivity matrices in health and disease. The…
In applications such as biological, social, and transportation networks, interactions between objects span multiple aspects. For accurately modeling such applications, multilayer networks have been proposed. Community search allows for…
Finding cohesive subgraphs in a large graph has many important applications, such as community detection and biological network analysis. Clique is often a too strict cohesive structure since communities or biological modules rarely form as…
A novel framework for consensus clustering is presented which has the ability to determine both the number of clusters and a final solution using multiple algorithms. A consensus similarity matrix is formed from an ensemble using multiple…