## A centrality measure for cycles and subgraphs II

Research output: Contribution to journalArticlepeer-review

### Standard

A centrality measure for cycles and subgraphs II. / Giscard, Pierre-Louis; Wilson, Richard Charles.

In: Applied Network Science, Vol. 3, No. 9, 08.06.2018.

Research output: Contribution to journalArticlepeer-review

### Harvard

Giscard, P-L & Wilson, RC 2018, 'A centrality measure for cycles and subgraphs II', Applied Network Science, vol. 3, no. 9. https://doi.org/10.1007/s41109-018-0064-5

### APA

Giscard, P-L., & Wilson, R. C. (2018). A centrality measure for cycles and subgraphs II. Applied Network Science, 3(9). https://doi.org/10.1007/s41109-018-0064-5

### Vancouver

Giscard P-L, Wilson RC. A centrality measure for cycles and subgraphs II. Applied Network Science. 2018 Jun 8;3(9). https://doi.org/10.1007/s41109-018-0064-5

### Author

Giscard, Pierre-Louis ; Wilson, Richard Charles. / A centrality measure for cycles and subgraphs II. In: Applied Network Science. 2018 ; Vol. 3, No. 9.

@article{37f6772ccf844d958db889fcdb764b3c,
title = "A centrality measure for cycles and subgraphs II",
abstract = "In a recent work we introduced a measure of importance for groups of vertices in a complex network. This centrality for groups is always between 0 and 1 and induces the eigenvector centrality over vertices. Furthermore, its value over any group is the fraction of all network flows intercepted by this group. Here we provide the rigorous mathematical constructions underpinning these results via a semi-commutative extension of a number theoretic sieve. We then established further relations between the eigenvector centrality and the centrality proposed here, showing that the latter is a proper extension of the former to groups of nodes. We finish by comparing the centrality proposed here with the notion of group-centrality introduced by Everett and Borgatti on two real-world networks: the Wolfe{\textquoteright}s dataset and the protein-protein interaction network of the yeast Saccharomyces cerevisiae. In this latter case, we demonstrate that the centrality is able to distinguish protein complexes",
author = "Pierre-Louis Giscard and Wilson, {Richard Charles}",
note = "{\textcopyright} The Author(s) 2018.",
year = "2018",
month = jun,
day = "8",
doi = "10.1007/s41109-018-0064-5",
language = "English",
volume = "3",
journal = "Applied Network Science",
issn = "2364-8228",
publisher = "Springer Open",
number = "9",

}

TY - JOUR

T1 - A centrality measure for cycles and subgraphs II

AU - Giscard, Pierre-Louis

AU - Wilson, Richard Charles

N1 - © The Author(s) 2018.

PY - 2018/6/8

Y1 - 2018/6/8

N2 - In a recent work we introduced a measure of importance for groups of vertices in a complex network. This centrality for groups is always between 0 and 1 and induces the eigenvector centrality over vertices. Furthermore, its value over any group is the fraction of all network flows intercepted by this group. Here we provide the rigorous mathematical constructions underpinning these results via a semi-commutative extension of a number theoretic sieve. We then established further relations between the eigenvector centrality and the centrality proposed here, showing that the latter is a proper extension of the former to groups of nodes. We finish by comparing the centrality proposed here with the notion of group-centrality introduced by Everett and Borgatti on two real-world networks: the Wolfe’s dataset and the protein-protein interaction network of the yeast Saccharomyces cerevisiae. In this latter case, we demonstrate that the centrality is able to distinguish protein complexes

AB - In a recent work we introduced a measure of importance for groups of vertices in a complex network. This centrality for groups is always between 0 and 1 and induces the eigenvector centrality over vertices. Furthermore, its value over any group is the fraction of all network flows intercepted by this group. Here we provide the rigorous mathematical constructions underpinning these results via a semi-commutative extension of a number theoretic sieve. We then established further relations between the eigenvector centrality and the centrality proposed here, showing that the latter is a proper extension of the former to groups of nodes. We finish by comparing the centrality proposed here with the notion of group-centrality introduced by Everett and Borgatti on two real-world networks: the Wolfe’s dataset and the protein-protein interaction network of the yeast Saccharomyces cerevisiae. In this latter case, we demonstrate that the centrality is able to distinguish protein complexes

U2 - 10.1007/s41109-018-0064-5

DO - 10.1007/s41109-018-0064-5

M3 - Article

VL - 3

JO - Applied Network Science

JF - Applied Network Science

SN - 2364-8228

IS - 9

ER -