Abstract
Centrality indices aim to quantify the importance of nodes or edges in a network. Much interest has been recently raised by the body of work in which a node's connectivity is understood less as its contribution to the quality or speed of communication in the network and more as its role in enabling communication altogether. Consequently, a node is assessed based on whether or not the network (or part of it) becomes disconnected if this node is removed. While these new indices deliver promising insights, to date very little is known about their theoretical properties. To address this issue, we propose an axiomatic approach. Specifically, we prove that there exists a unique centrality index satisfying a number of desirable properties. This new index, which we call the Attachment centrality, is equivalent to the Myerson value of a certain graph-restricted game. Building upon our theoretical analysis we show that, while computing the Attachment centrality is #P-complete, it has certain computational properties that are more attractive than the Myerson value for an arbitrary game. In particular, it can be computed in chordal graphs in polynomial time.
| Original language | English |
|---|---|
| Pages (from-to) | 151-179 |
| Number of pages | 29 |
| Journal | Artificial Intelligence |
| Volume | 274 |
| DOIs | |
| Publication status | Published - Sep 1 2019 |
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All Science Journal Classification (ASJC) codes
- Language and Linguistics
- Linguistics and Language
- Artificial Intelligence
Cite this
Attachment centrality : Measure for connectivity in networks. / Skibski, Oskar; Rahwan, Talal; Michalak, Tomasz P.; Yokoo, Makoto.
In: Artificial Intelligence, Vol. 274, 01.09.2019, p. 151-179.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Attachment centrality
T2 - Measure for connectivity in networks
AU - Skibski, Oskar
AU - Rahwan, Talal
AU - Michalak, Tomasz P.
AU - Yokoo, Makoto
PY - 2019/9/1
Y1 - 2019/9/1
N2 - Centrality indices aim to quantify the importance of nodes or edges in a network. Much interest has been recently raised by the body of work in which a node's connectivity is understood less as its contribution to the quality or speed of communication in the network and more as its role in enabling communication altogether. Consequently, a node is assessed based on whether or not the network (or part of it) becomes disconnected if this node is removed. While these new indices deliver promising insights, to date very little is known about their theoretical properties. To address this issue, we propose an axiomatic approach. Specifically, we prove that there exists a unique centrality index satisfying a number of desirable properties. This new index, which we call the Attachment centrality, is equivalent to the Myerson value of a certain graph-restricted game. Building upon our theoretical analysis we show that, while computing the Attachment centrality is #P-complete, it has certain computational properties that are more attractive than the Myerson value for an arbitrary game. In particular, it can be computed in chordal graphs in polynomial time.
AB - Centrality indices aim to quantify the importance of nodes or edges in a network. Much interest has been recently raised by the body of work in which a node's connectivity is understood less as its contribution to the quality or speed of communication in the network and more as its role in enabling communication altogether. Consequently, a node is assessed based on whether or not the network (or part of it) becomes disconnected if this node is removed. While these new indices deliver promising insights, to date very little is known about their theoretical properties. To address this issue, we propose an axiomatic approach. Specifically, we prove that there exists a unique centrality index satisfying a number of desirable properties. This new index, which we call the Attachment centrality, is equivalent to the Myerson value of a certain graph-restricted game. Building upon our theoretical analysis we show that, while computing the Attachment centrality is #P-complete, it has certain computational properties that are more attractive than the Myerson value for an arbitrary game. In particular, it can be computed in chordal graphs in polynomial time.
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UR - http://www.scopus.com/inward/citedby.url?scp=85063961938&partnerID=8YFLogxK
U2 - 10.1016/j.artint.2019.03.002
DO - 10.1016/j.artint.2019.03.002
M3 - Article
VL - 274
SP - 151
EP - 179
JO - Artificial Intelligence
JF - Artificial Intelligence
SN - 0004-3702
ER -