Finding clique clusters with the highest betweenness centrality

Rysz, Maciej; Pajouh, Foad Mahdavi; Pasiliao, Eduardo L.

doi:10.1016/j.ejor.2018.05.006

Cited by 19 publications

(10 citation statements)

References 23 publications

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“…Moreover, let

γ_{i j} (S, S^{'})

denote the total number of shortest paths between i and j whose intersection with set S is equal to set

S^{'}

. We then have the following Proposition 1, based on [33].…”

Section: Formulationsmentioning

confidence: 99%

“…We specifically focus on the contributions in [40] and [41], as some of the problems formally generalized here were seen as special cases in these previous works. We also adapt some of the results presented in [33] to apply to our setup.…”

Section: Introductionmentioning

confidence: 99%

“…This realization motivated a series of works that extend standard centrality metrics to groups and classes (see, e.g., [7,11,12,39]). This further motivated research in groups that induce specific structures or cohesiveness requirements [27,33,40,41,46]. We specifically focus on the contributions in [40] and [41], as some of the problems formally generalized here were seen as special cases in these previous works.…”

Section: Introductionmentioning

confidence: 99%

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Novel centrality metrics for studying essentiality in protein‐protein interaction networks based on group structures

Rasti

Vogiatzis

2021

Networks

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In this work, we introduce centrality metrics based on group structures, and we show their performance in estimating importance in protein-protein interaction networks (PPINs). The centrality metrics introduced are extensions of well-known nodal metrics. However, instead of focusing on a single node, we focus on that node and the set of nodes around it. Furthermore, we require the set of nodes to induce a specific pattern or structure. The structures investigated range from the "stricter" induced stars and cliques, to a "looser" definition of a representative structure. We derive the computational complexity of all metrics and provide mixed integer programming formulations; due to the problem complexity and the size of PPINs, using commercial solvers is not always viable. Hence, we propose a combinatorial branch-and-bound solution approach. We conclude by showing the effectiveness of the proposed metrics in identifying essential proteins in Helicobacter pylori and comparing them to nodal metrics.

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“…Moreover, let

γ_{i j} (S, S^{'})

denote the total number of shortest paths between i and j whose intersection with set S is equal to set

S^{'}

. We then have the following Proposition 1, based on [33].…”

Section: Formulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Novel centrality metrics for studying essentiality in protein‐protein interaction networks based on group structures

Rasti

Vogiatzis

2021

Networks

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“…More recently, researchers have focused on highest betweenness groups [39]. Finally, another extension of identifying highly centralized groups has to do with the added restriction that the group induces a subgraph "motif ", such as being a complete subgraph/clique [40,41], or inducing a star [42].…”

Section: Definitions and Notationmentioning

confidence: 99%

Maximum Closeness Centrality k-Clubs: A Study of Dock-Less Bike Sharing

Taleqani

Vogiatzis

Hough

2020

Journal of Advanced Transportation

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In this work, we investigate a new paradigm for dock-less bike sharing. Recently, it has become essential to accommodate connected and free-floating bicycles in modern bike-sharing operations. This change comes with an increase in the coordination cost, as bicycles are no longer checked in and out from bike-sharing stations that are fully equipped to handle the volume of requests; instead, bicycles can be checked in and out from virtually anywhere. In this paper, we propose a new framework for combining traditional bike stations with locations that can serve as free-floating bike-sharing stations. The framework we propose here focuses on identifying highly centralized k-clubs (i.e., connected subgraphs of restricted diameter). The restricted diameter reduces coordination costs as dock-less bicycles can only be found in specific locations. In addition, we use closeness centrality as this metric allows for quick access to dock-less bike sharing while, at the same time, optimizing the reach of service to bikers/customers. For the proposed problem, we first derive its computational complexity and show that it is NP-hard (by reduction from the 3-SATISFIABILITY problem), and then provide an integer programming formulation. Due to its computational complexity, the problem cannot be solved exactly in a large-scale setting, as is such of an urban area. Hence, we provide a greedy heuristic approach that is shown to run in reasonable computational time. We also provide the presentation and analysis of a case study in two cities of the state of North Dakota: Casselton and Fargo. Our work concludes with the cost-benefit analysis of both models (docked vs. dockless) to suggest the potential advantages of the proposed model.

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“…For example, finding the most central (in terms of the GBC) group of vertices that form a κ-club is considered in [9], where a group of vertices form a κ-club if the distance between any two members of the group is less than or equal to κ. Similarly, [9] and [64] The problem of finding a group of vertices of a given size g in a network that has the highest GBC is in general an NP-hard problem [7]. Brandes [4] and Puzis et al [8] propose algorithms to compute the GBC of any given group of vertices.…”

Section: Group Betweenness Centralitymentioning

confidence: 99%

k-step betweenness centrality

Akgün

Tural

2019

Comput Math Organ Theory

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, 90 pages The notions of betweenness centrality (BC) and its extension group betweenness centrality (GBC) are widely used in social network analyses. We introduce variants of them; namely, the k-step BC and k-step GBC. The k-step GBC of a group of vertices in a network is a measure of the likelihood that at least one group member will get the information communicated between a randomly chosen pair of vertices through a randomly chosen shortest path within the first k steps of the start of the communication. The k-step GBC of a single vertex is the k-step BC of that vertex. The introduced centrality measures may find uses in applications where it is important or critical to obtain the information within a fixed time of the start of the communication. For the introduced centrality measures, we propose an algorithm that can compute successively the k-step GBC of several groups of vertices. Moreover, we propose a mixed integer programming formulation to compute the group that has the highest k-step GBC value and a heuristic approach to compute a group of vertices whose k-step GBC value is high. The performances of the proposed algorithms are evaluated through computational experiments on real and randomly generated networks.

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Finding clique clusters with the highest betweenness centrality

Cited by 19 publications

References 23 publications

Novel centrality metrics for studying essentiality in protein‐protein interaction networks based on group structures

Novel centrality metrics for studying essentiality in protein‐protein interaction networks based on group structures

Maximum Closeness Centrality k-Clubs: A Study of Dock-Less Bike Sharing

k-step betweenness centrality

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