The stochastic pseudo-star degree centrality problem

Camur, Mustafa Can; Sharkey, Thomas C.; Vogiatzis, Chrysafis

doi:10.1016/j.ejor.2022.11.042

Cited by 7 publications

(5 citation statements)

References 41 publications

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“…The algorithm was tested on both simulated small‐world graphs and a natural protein‐to‐protein interaction network. The results showed that the proposed Benders Decomposition algorithm was both faster and produced higher quality results, demonstrating the significance of this new centrality metric in detecting essential proteins 8 …”

Section: Related Workmentioning

confidence: 93%

“…The results showed that the proposed Benders Decomposition algorithm was both faster and produced higher quality results, demonstrating the significance of this new centrality metric in detecting essential proteins. 8 In uncertain graphs, closeness centrality is a crucial measure that considers uncertainties in graph data. The focus is on the "batch closeness centrality calculation" problem, which calculates the closeness centrality for a specific subset of vertices.…”

Section: Related Workmentioning

confidence: 99%

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Identification of influential vertices in complex networks: A hitting time‐based approach

Kumar,

Singh,

Sharma

2024

Concurrency and Computation

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Unravelling the dynamics of network vertices is pivotal, and traditional centrality measures have limitations in adapting to structural changes, directed and weighted networks, and temporal analyses. This paper introduces a ground breaking approach ‐ hitting time‐based centrality. Utilizing network matrix notations and a random walk model on a connected network , we establish a Markov chain to quantify the hitting time, hitting distance, and hitting centrality, providing a nuanced measure prioritizing central vertices. Through extensive experiments using Kendall's tau coefficient, the paper evaluates the method's correlation with actual influence in the Susceptible‐Infectious (SI) model, showcasing superior performance across diverse network sizes and structures. The hitting centrality method exhibits sensitivity to connectivity dynamics, effective incorporation of temporal dynamics, and robust handling of weighted and directed networks. Positive Kendall's tau coefficients underline the method's proficiency in prioritizing influential vertices by correlating hitting centrality values with actual infection ability. The demonstrated robustness to structural changes enhances its utility for dynamic network analysis. In conclusion, our hitting time‐based centrality approach emerges as a promising method, mitigating the shortcomings of traditional measures. By integrating information propagation speed, accommodating network dynamics, and enabling time‐dependent analyses, it offers a comprehensive tool for evaluating vertex importance and influence in complex networks.

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Section: Related Workmentioning

confidence: 93%

Section: Related Workmentioning

confidence: 99%

Identification of influential vertices in complex networks: A hitting time‐based approach

Kumar,

Singh,

Sharma

2024

Concurrency and Computation

View full text Add to dashboard Cite

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“…Unsurprisingly, in 2023, we witness even more studies in group centrality research. To start with, Camur et al (2023) integrates probability values regarding edge connectivity and introduce the very first "probabilistic" group centrality metric as stochastic pseudo-star degree centrality. According to the authors a pseudo-star is a set of nodes forming a star with at least a probability θ ∈ [0, 1].…”

Section: Brief History On Group Centralitymentioning

confidence: 99%

“…Conversely, research related to highest degree star centrality frequently employ decomposition algorithms to solve the large-scale models. In both Camur et al (2022) and Camur et al (2023), the authors implement various Benders decomposition strategies, including traditional Benders approach, modern Benders, two-phase, three-phase decomposition, and Logical Benders. The problems of star centrality with the highest closeness and betweenness, on the other hand, are tackled by CBB approaches.…”

Section: Structures and Computational Approachesmentioning

confidence: 99%

“…Returning to the pseudo-star degree centrality problem (Camur et al, 2023), this novel group centrality metric is shown to be more effective than its deterministic correspondent (i.e., SDC, see Vogiatzis and Camur (2019)) in determining essential proteins in protein-protein interaction networks. That said, it is important to note that this study does not employ any stochastic optimization modeling or techniques.…”

Section: Brief History On Group Centralitymentioning

confidence: 99%

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The Star Degree Centrality Problem: A Decomposition Approach

Camur

Sharkey

Vogiatzis

2022

INFORMS Journal on Computing

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We consider the problem of identifying the induced star with the largest cardinality open neighborhood in a graph. This problem, also known as the star degree centrality (SDC) problem, is shown to be [Formula: see text]-complete. In this work, we first propose a new integer programming (IP) formulation, which has a smaller number of constraints and nonzero coefficients in them than the existing formulation in the literature. We present classes of networks in which the problem is solvable in polynomial time and offer a new proof of [Formula: see text]-completeness that shows the problem remains [Formula: see text]-complete for both bipartite and split graphs. In addition, we propose a decomposition framework that is suitable for both the existing and our formulations. We implement several acceleration techniques in this framework, motivated by techniques used in Benders decomposition. We test our approaches on networks generated based on the Barabási–Albert, Erdös–Rényi, and Watts–Strogatz models. Our decomposition approach outperforms solving the IP formulations in most of the instances in terms of both solution time and quality; this is especially true for larger and denser graphs. We then test the decomposition algorithm on large-scale protein–protein interaction networks, for which SDC is shown to be an important centrality metric. Summary of Contribution: In this study, we first introduce a new integer programming (NIP) formulation for the star degree centrality (SDC) problem in which the goal is to identify the induced star with the largest open neighborhood. We then show that, although the SDC can be efficiently solved in tree graphs, it remains [Formula: see text]-complete in both split and bipartite graphs via a reduction performed from the set cover problem. In addition, we implement a decomposition algorithm motivated by Benders decomposition together with several acceleration techniques to both the NIP formulation and the existing formulation in the literature. Our experimental results indicate that the decomposition implementation on the NIP is the best solution method in terms of both solution time and quality.

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A survey on optimization studies of group centrality metrics

Camur,

Vogiatzis

2024

Networks

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Centrality metrics have become a popular concept in network science and optimization. Over the years, centrality has been used to assign importance and identify influential elements in various settings, including transportation, infrastructure, biological, and social networks, among others. That said, most of the literature has focused on nodal versions of centrality. Recently, group counterparts of centrality have started attracting scientific and practitioner interest. The identification of sets of nodes that are influential within a network is becoming increasingly more important. This is even more pronounced when these sets of nodes are required to induce a certain motif or structure. In this study, we review group centrality metrics from an operations research and optimization perspective for the first time. This is particularly interesting due to the rapid evolution and development of this area in the operations research community over the last decade. We first present a historical overview of how we have reached this point in the study of group centrality. We then discuss the different structures and motifs that appear prominently in the literature, alongside the techniques and methodologies that are popular. We finally present possible avenues and directions for future work, mainly in three areas: (i) probabilistic metrics to account for randomness along with stochastic optimization techniques; (ii) structures and relaxations that have not been yet studied; and (iii) new emerging applications that can take advantage of group centrality. Our survey offers a concise review of group centrality and its intersection with network analysis and optimization.

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The stochastic pseudo-star degree centrality problem

Cited by 7 publications

References 41 publications

Identification of influential vertices in complex networks: A hitting time‐based approach

Identification of influential vertices in complex networks: A hitting time‐based approach

The Star Degree Centrality Problem: A Decomposition Approach

A survey on optimization studies of group centrality metrics

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