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research
On the Analysis of a Label Propagation Algorithm for Community Detection
Authors
Kishore Kothapalli
Sriram V. Pemmaraju
Vivek Sardeshmukh
Publication date
13 October 2012
Publisher
View
on
arXiv
Abstract
This paper initiates formal analysis of a simple, distributed algorithm for community detection on networks. We analyze an algorithm that we call \textsc{Max-LPA}, both in terms of its convergence time and in terms of the "quality" of the communities detected. \textsc{Max-LPA} is an instance of a class of community detection algorithms called \textit{label propagation} algorithms. As far as we know, most analysis of label propagation algorithms thus far has been empirical in nature and in this paper we seek a theoretical understanding of label propagation algorithms. In our main result, we define a clustered version of \er random graphs with clusters
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1
,
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2
,
.
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.
,
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V_1, V_2,..., V_k
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1
β
,
V
2
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,
...
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V
k
β
where the probability
p
p
p
, of an edge connecting nodes within a cluster
V
i
V_i
V
i
β
is higher than
p
β²
p'
p
β²
, the probability of an edge connecting nodes in distinct clusters. We show that even with fairly general restrictions on
p
p
p
and
p
β²
p'
p
β²
(
p
=
Ξ©
(
1
n
1
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4
β
Ο΅
)
p = \Omega(\frac{1}{n^{1/4-\epsilon}})
p
=
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(
n
1/4
β
Ο΅
1
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)
for any
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Ο΅
>
0
,
p
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=
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(
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2
)
p' = O(p^2)
p
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=
O
(
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2
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, where
n
n
n
is the number of nodes), \textsc{Max-LPA} detects the clusters
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,
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2
,
.
.
.
,
V
n
V_1, V_2,..., V_n
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1
β
,
V
2
β
,
...
,
V
n
β
in just two rounds. Based on this and on empirical results, we conjecture that \textsc{Max-LPA} can correctly and quickly identify communities on clustered \er graphs even when the clusters are much sparser, i.e., with
p
=
c
log
β‘
n
n
p = \frac{c\log n}{n}
p
=
n
c
l
o
g
n
β
for some
c
>
1
c > 1
c
>
1
.Comment: 17 pages. Submitted to ICDCN 201
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Last time updated on 30/10/2017