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One of the most fundamental problems in large scale network analysis is to determine the importance of a particular node in a network. Betweenness centrality is the most widely used metric to measure the importance of a node in a network.…
Measures of complex network analysis, such as vertex centrality, have the potential to unveil existing network patterns and behaviors. They contribute to the understanding of networks and their components by analyzing their structural…
Given a connected graph $G=(V,E)$, the closeness centrality of a vertex $v$ is defined as $\frac{n-1}{\sum_{w \in V} d(v,w)}$. This measure is widely used in the analysis of real-world complex networks, and the problem of selecting the $k$…
Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were…
We develop efficient parameterized, with additive error, approximation algorithms for the (Connected) $r$-Domination problem and the (Connected) $p$-Center problem for unweighted and undirected graphs. Given a graph $G$, we show how to…
Only when understanding hackers' tactics, can we thwart their attacks. With this spirit, this paper studies how hackers can effectively launch the so-called 'targeted node attacks', in which iterative attacks are staged on a network, and in…
Motivated by an application from geodesy, we introduce a novel clustering problem which is a $k$-center (or k-diameter) problem with a side constraint. For the side constraint, we are given an undirected connectivity graph $G$ on the input…
We study the problem of maximizing a submodular function, subject to a cardinality constraint, with a set of agents communicating over a connected graph. We propose a distributed greedy algorithm that allows all the agents to converge to a…
In this paper we are interested in a version of the All-pairs Shortest Paths problem (APSP) that fits neither in the exact nor in the approximate case. We define a measure of centrality of a shortest path, related to the ``importance'' of…
In network analysis and graph mining, closeness centrality is a popular measure to infer the importance of a vertex. Computing closeness efficiently for individual vertices received considerable attention. The NP-hard problem of group…
Critical nodes in networks are extremely vulnerable to malicious attacks to trigger negative cascading events such as the spread of misinformation and diseases. Therefore, effective moderation of critical nodes is very vital for mitigating…
Viral marketing campaigns seek to recruit the most influential individuals to cover the largest target audience. This can be modeled as the well-studied maximum coverage problem. There is a related problem when the recruited nodes are…
How does one find important or influential people in an online social network? Researchers have proposed a variety of centrality measures to identify individuals that are, for example, often visited by a random walk, infected in an…
Betweenness is a well-known centrality measure that ranks the nodes according to their participation in the shortest paths of a network. In several scenarios, having a high betweenness can have a positive impact on the node itself. Hence,…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
We consider the Max Unique Coverage problem, including applications to the data stream model. The input is a universe of $n$ elements, a collection of $m$ subsets of this universe, and a cardinality constraint, $k$. The goal is to select a…
A variety of metrics have been proposed to measure the relative importance of nodes in a network. One of these, alpha-centrality [Bonacich, 2001], measures the number of attenuated paths that exist between nodes. We introduce a normalized…
This paper is concerned with distributed detection of central nodes in complex networks using closeness centrality. Closeness centrality plays an essential role in network analysis. Evaluating closeness centrality exactly requires complete…
Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to…
Concomitant with the tremendous prevalence of online social media platforms, the interactions among individuals are unprecedentedly enhanced. People are free to interact with acquaintances, express and exchange their own opinions through…