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Abstract
Modularity is designed to measure the strength of a division of a network into clusters. For
n
∈
ℕ , consider
a set
S of
n elements. Let
V be the set of all
subsets of
S of
size
r . Consider
the graph
G ( n , r , s )
with vertices
V
and edges that connect two vertices if and only if their intersection has size
s . In this article, we find
the exact modularity of
G ( n , 2 , 1 )
for
n
≥ 5 .
Keywords
modularity, line graphs, Johnson graphs
Mathematical Subject Classification
Primary: 05C76
Milestones
Received: 14 May 2020
Revised: 12 July 2020
Accepted: 27 July 2020
Published: 16 January 2021