Next Article in Journal
An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations
Previous Article in Journal
A New Continuous-Discrete Fuzzy Model and Its Application in Finance
Open AccessArticle

Group Degree Centrality and Centralization in Networks

by Matjaž Krnc 1,† and Riste Škrekovski 1,2,3,*,†
1
FAMNIT, University of Primorska, 6000 Koper, Slovenia
2
Faculty of Information Studies, 8000 Novo Mesto, Slovenia
3
Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljna, Slovenia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(10), 1810; https://doi.org/10.3390/math8101810
Received: 7 September 2020 / Revised: 2 October 2020 / Accepted: 10 October 2020 / Published: 16 October 2020
(This article belongs to the Section Network Science)
The importance of individuals and groups in networks is modeled by various centrality measures. Additionally, Freeman’s centralization is a way to normalize any given centrality or group centrality measure, which enables us to compare individuals or groups from different networks. In this paper, we focus on degree-based measures of group centrality and centralization. We address the following related questions: For a fixed k, which k-subset S of members of G represents the most central group? Among all possible values of k, which is the one for which the corresponding set S is most central? How can we efficiently compute both k and S? To answer these questions, we relate with the well-studied areas of domination and set covers. Using this, we first observe that determining S from the first question is NP-hard. Then, we describe a greedy approximation algorithm which computes centrality values over all group sizes k from 1 to n in linear time, and achieve a group degree centrality value of at least (11/e)(w*k), compared to the optimal value of w*. To achieve fast running time, we design a special data structure based on the related directed graph, which we believe is of independent interest. View Full-Text
Keywords: vertex degree; group centrality; freeman centralization vertex degree; group centrality; freeman centralization
Show Figures

Figure 1

MDPI and ACS Style

Krnc, M.; Škrekovski, R. Group Degree Centrality and Centralization in Networks. Mathematics 2020, 8, 1810.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop