Abstract
This paper studies the problem of finding graphs that locally maximize the clustering coefficient in the space of graphs with a fixed degree sequence. Such a graph is characterized by the property that the clustering coefficient cannot be increased, no matter how a single 2-switch is applied. First, an explicit formula for the amount of change in the clustering coefficient of a graph caused by a single 2-switch is given. Next, some classes of graphs with the property stated above are presented. An example of such a graph is the one obtained from a tree by replacing its edges with cliques with the same order.
| Original language | English |
|---|---|
| Pages (from-to) | 525-535 |
| Number of pages | 11 |
| Journal | Discrete Applied Mathematics |
| Volume | 217 |
| DOIs | |
| Publication status | Published - Jan 30 2017 |
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Keywords
- 2-switch
- Clustering coefficient
- Complex network
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics
Cite this
Graphs that locally maximize clustering coefficient in the space of graphs with a fixed degree sequence. / Fukami, Tatsuya; Takahashi, Norikazu.
In: Discrete Applied Mathematics, Vol. 217, 30.01.2017, p. 525-535.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Graphs that locally maximize clustering coefficient in the space of graphs with a fixed degree sequence
AU - Fukami, Tatsuya
AU - Takahashi, Norikazu
PY - 2017/1/30
Y1 - 2017/1/30
N2 - This paper studies the problem of finding graphs that locally maximize the clustering coefficient in the space of graphs with a fixed degree sequence. Such a graph is characterized by the property that the clustering coefficient cannot be increased, no matter how a single 2-switch is applied. First, an explicit formula for the amount of change in the clustering coefficient of a graph caused by a single 2-switch is given. Next, some classes of graphs with the property stated above are presented. An example of such a graph is the one obtained from a tree by replacing its edges with cliques with the same order.
AB - This paper studies the problem of finding graphs that locally maximize the clustering coefficient in the space of graphs with a fixed degree sequence. Such a graph is characterized by the property that the clustering coefficient cannot be increased, no matter how a single 2-switch is applied. First, an explicit formula for the amount of change in the clustering coefficient of a graph caused by a single 2-switch is given. Next, some classes of graphs with the property stated above are presented. An example of such a graph is the one obtained from a tree by replacing its edges with cliques with the same order.
KW - 2-switch
KW - Clustering coefficient
KW - Complex network
UR - http://www.scopus.com/inward/record.url?scp=85001784669&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85001784669&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2016.10.002
DO - 10.1016/j.dam.2016.10.002
M3 - Article
AN - SCOPUS:85001784669
VL - 217
SP - 525
EP - 535
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
ER -