Community Detection with Networkx

Community Structures
Erika Fille T. Legara, Ph.D.
@eﬂegara | h5p://eﬂegara.github.io
Scien&st, IHPC-A*STAR
http://tiny.cc/commdet2017
http://tinyurl.com/commdet2017

Walkthrough
•  Network structure and function
•  Communities
•  Community detection algorithms
•  Divisive
•  Agglomeratxive
•  Application: Community detection in framing analysis
•  Hands-on http://tiny.cc/commdet2017

Network Structure
•  Path length
•  Diameter
•  Clustering coeﬃcient
•  Degree distribution
•  Centrality measures
Community Structures | EF Legara | 2016 NTU Winter School on Complexity Science
What would the behaviour of
networked systems be based on their
structural properties?
Structure Func*on

Communities
•  Cluster, module, group
•  A group of nodes that have a
higher likelihood of connecting
to each other than to nodes
from other communities

Example of Communities
•  Network: World Wide Web
•  Communities: Sites on related topics
•  Network: Friendship network
•  Communities: Group formation among people
•  Network: Metabolic networks
•  Communities: Functional modules
•  Network: Collaboration network
•  Communities: Research ﬁelds

Social Networks: Politics, Ideologies
The political blogosphere and the 2004 U.S. election:
divided they blog
by Lada Adamic, Natalie Glance
Social media, political change and the #RapplerDebate
by Maria A. Ressa and Russell Shepherd

How does one ﬁnd the
Communities?

Zachary’s karate club
34 members of a karate club
78 pairwise links between members who
interacted outside the club
“Mr. Hi”
“John A”

Methods
Agglomera]ve Divisive
Cut 3 classes
Cut 4 classes
Cut 6 classes

Modularity
•  Measure the quality of a partition
“the fraction of edges that fall within communities, minus the
expected value of the same quantity if edges fall at random
without regard for the community structure”
Mc =
ncX
c=1
"
Lc
L
✓
kc
2L
◆2
#

Modularity
Mc =
ncX
c=1
"
Lc
L
✓
kc
2L
◆2
#
Number of
communities
Total number
of links in
Community c
Total node
degrees in
Community c
Total number of
links

Modularity
Mc =
ncX
c=1
"
Lc
L
✓
kc
2L
◆2
#
Number of
communities
Total number
of links in
Community c
Total node
degrees in
Community c
Total number of
links
1 2
3
Community 1:
"
6
20
✓
14
40
◆2
#
"
4
20
✓
10
40
◆2
#
Community 3:
Mc = 0.50
Community 2:
"
7
20
✓
16
40
◆2
#

Modularity
Mc =
ncX
c=1
"
Lc
L
✓
kc
2L
◆2
#
Number of
communities
Total number
of links in
Community c
Total node
degrees in
Community c
Total number of
links
1 2
3
Mc = 0.35
Community 1:
"
4
20
✓
10
40
◆2
#
Community 3:
"
2
20
✓
8
40
◆2
#
Community 2:
"
9
20
✓
22
40
◆2
#

Modularity
Mc =
ncX
c=1
"
Lc
L
✓
kc
2L
◆2
#
Number of
communities
Total number
of links in
Community c
Total node
degrees in
Community c
Total number of
links
M = 0

1 2
3
Mc = 0.50
M = 0
1 2
3
Mc = 0.35
Optimal Partition Suboptimal Partition
One Community
Modularity
Mc =
ncX
c=1
"
Lc
L
✓
kc
2L
◆2
#

Quantifying Community Structures
Divisive
•  Girvan-Newman Algorithm (edge betweenness)
Agglomerative
•  Hierarchical clustering (distance matrix)
•  Louvain Method (modularity-maximization)
Cut 3 classes
Cut 4 classes
Cut 6 classes

Community Detection in Framing Analysis
Framing - the “central organizing idea for
making sense of an issue or conﬂict and
suggesting what is at stake”
EF Legara, C Monterola, C David, and JM Atun, "News Framing of
Population and Family Planning Issues via Syntactic Network
Analysis", Intl J of Mod Phys C 21, Issue: 1, pp. 51-65 (2010).
A Network of Words

“Frames have been shown experimentally to cause diﬀerences
in attributions of responsibility among readers or audiences.”

•  346 news articles (randomly sampled)
•  Population, family planning, reproductive health, and
contraception published between 1987 and 2007
Framing in the News

Every article assigned to
a single dominant frame
q Population and Development
q Family Planning as Conﬂict between
Government and Church
q Women’s and Reproductive Health
q Population Management Threatens
Morals and Values
q Population Growth and
Demographic Trends
q Others

Collected Articles
Delete stop words and replace
with placeholder “xxx”
Generalize conceptually
similar terms
Obtain high-frequency words
A Network of Words

Map words: add edge weight
(1u) between nodes if words co-
exist in a scanning window
Create co-occurrence
network
Perform cluster analysis

Co-Occurrence
Network of
Words

F1: Popula]on and Development
F2: Popula]on Growth and
Demographic Trends
F3: Women’s and Reproduc]ve Health
F4: Family Planning as Conﬂict
between Government and Church
F5: Popula]on Management
Threatens Morals and Values
F6: Others
Development Frame
Maternal Health Frame
Framing by the Church
F1: Popula]on and Development
F2: Popula]on Growth and
Demographic Trends
F3: Women’s and Reproduc]ve Health
F4: Family Planning as Conﬂict
between Government and Church
F5: Popula]on Management
Threatens Morals and Values
F6: Others
Coding done by communica*on
research experts

http://tinyurl.com/NetStruc2016
http://tiny.cc/NetStruc2016

Community Structures
Erika Fille T. Legara, Ph.D.
@eﬂegara
Scien&st, IHPC-A*STAR
http://tiny.cc/commdet2017

Community Detection with Networkx

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