Formulation of modularity factor for community detection applying

INTERNATIONALComputer Engineering and Technology ENGINEERING
International Journal of JOURNAL OF COMPUTER (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 2, March – April (2013), © IAEME
& TECHNOLOGY (IJCET)

ISSN 0976 – 6367(Print)
ISSN 0976 – 6375(Online) IJCET
Volume 4, Issue 2, March – April (2013), pp. 135-141
© IAEME: www.iaeme.com/ijcet.asp
Journal Impact Factor (2013): 6.1302 (Calculated by GISI)
©IAEME
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FORMULATION OF MODULARITY FACTOR FOR COMMUNITY
DETECTION APPLYING MULTIRESOLUTION ON MOI
ALGORITHM

K. Senthil Kumar1, K. S. Suganthi2, C. Suchitra3, S. Sharmili4
1
(Assistant Professor, Department of Information Technology, SMVEC, Pondicherry, India)
2
(Department of Information Technology, SMVEC, Pondicherry, India)
3
4

ABSTRACT

Community structure is one of the most important properties in social networks,
and has received an enormous amount of attention in recent years. Community Detection,
a form of clustering, is a technique which is used for the discovery of the naturally
occurring associations between vertices in a given network. Initially, algorithms were
developed with the intention of detecting communities in static networks. This slowly
evolved into detecting communities in dynamic environments as the nature of the network
itself, in general, is dynamic. Community detection in dynamic networks with better
performance and better accuracy is a problem for which the authors have proposed an
idea involving the combination of two techniques: local community measurement of
multi resolution applied in multi – objective immune algorithm, replacing the current
local search strategy. Also, this proposal is phase one of the algorithm as the second
phase is still under work, without which the complete solution cannot be resolved.

Keywords: Community Detection, Graph Partition, Modularity, Networking

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International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-

I. INTRODUCTION

In recent years, the research on social networks is gaining utmost importance. Social
networks are usually represented by graphs where nodes represent individuals and edges
represent relationships and interactions among individuals. Community Detection is sometimes
also referred to as clustering, but we largely avoid this term to prevent confusion. Both Graph
Partitioning and community detection refer to the division of vertices in a network into groups or
clusters or communities. Such groups are tightly knit with many edges inside groups and only a
few edges between the groups. The ability to discover groups or cluster within a network proves
to be a useful tool for revealing the network’s structure and organization at a larger scale than of a
single vector. Clusters can also be defined as the group of vertices having association between the
vertices based on certain identified similarity. The basic formation or the initial representation of
communities was hierarchical clustering. The defect with hierarchical clustering was that they
had overlapping communities in their clusters. This is a disadvantage because; the idea of
community detection was developed so as to provide better understanding of the network
structure and organization when viewed by a network administrator for its activities. But this is
possible only if the communities are non – overlapping. Non – overlapping communities refer to
those communities in which the vertices of one community are present solely in that community.
In hierarchical clustering the vertices are clustered together but they do not form a coherent
network upon completion. As we have overlapping communities in hierarchical clustering, it is
not efficient as its latter developments of graph partitioning and community detection. Hence the
methods of graph partitioning and community detection of networks came into existence.
Graph partitioning is a classic problem of dividing the vertices of a network into non –
overlapping groups of given sizes so that number of edges between groups is minimized. The
main disadvantage in graph partitioning is that it is expected to specify the size of the community
and the number of communities in the network. Community Detection is a method that searches
for naturally occurring groups in a network without any regard to their size or number. This is
used for discovering and understanding the large scale structure of networks. The advantage is
that the number and the size of the communities are not fixed and the size of the community need
not be specified. One of the most widely used methods is simulated annealing. But it has the
drawback of being slow. Another general optimization method is genetic algorithm. It provides
high quality results but is also very slow. This method is applicable to a network of few 100
vertices. The third method is by using greedy algorithm and it is simple. This gives a reasonable
division of networks but the modularity values achieved are lower than those obtained by the
previous methodologies. But the runtime is the best of any current algorithm.
Multi-Objective evolutionary algorithm aims in the integration of dynamic and multi
objective algorithms in dynamic environments. It uses genetic mechanism – locus based
adjacency encoding scheme. Dynamic changing nature is not considered. A multi objective
immune algorithm can solve the community detection problem in dynamic social networks. Its
objective is to maximize the community quality and minimize the temporal cost. It can achieve
better accuracy in community extraction and capture community evolution more faithfully.
Online multi-resolution algorithm can identify both overlapping and non-overlapping
communities. It is fast and scalable in large-scale networks. It can be used freely to acquire
communities at any resolution. The contents mentioned above give an insight into the
proceedings so far in the domain of community detection. The purpose of this paper is to resolve
the disadvantages met in the previous methodologies followed for community detection.

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International Journal of Computer Engineering and Technology (IJCET), ISSN 0976- 0976

II. ARCHITECTURE DIAGRAM

The proposed model for the implementation of multiresolution parameters in multi
multiresolution
objective immune algorithm consists of three modules. The initial input network is integrated
with the first module where the modularity and betweenness values are calculated, the
modularity is calculated by Newman – Girvan formula of,
k
 l  d i 
2 
∑  i − 
 L

 2 L 


i=1  
The basic calculation of betweenness centrality is done by the formula,
formula
n (n − 1 )
2
The second module is associated with the identification of high similarity vertex
pairs. This is done so as to segregate them separately from the other vertices in the chosen
network. But the process does not stop there as the remaining vertices have to be segregated
using the same methodology. It is a cyclic process until all similar vertices have been
segregated.

Fig. 1: Architecture Design of the Proposed Model
:

The process starts under three conditions. Consider Qn to be the modularity factor that
has been calculated using the Newman – Girvan formula for modularity, we have,

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• Qm <= -1, indicating that the community so formed will be a weak structure
and can be easily subjected to frequent changes resulting in the instability.
• Qm = 0, indicating that no more community structures can be extracted from
the given network.
• Qm >= 1, indicating that the structures so formed are strong and are not
subjected to any frequent changes.
In the third module, there exists the regrouping of the isolated vertices based on the
high similarity of their respective modularity values. This finally gives us the required output
network.

III. ALGORITHM FOR MODULARITY CALCULATION

In context with social networking that can be best cited for the concept proposed the
parameters taken into consideration includes tags in the photos posted, comments received on
the photos posted and related posts that have been shared or agreed upon. There are the
parameters that help in calculating the parameter that helps in calculating the edges cost
between two vertices. This helps in analyzing the strength of the link of the considered
network. The algorithm given below has been developed with the Newman – Girvan as its
base.

Input: Text file containing the cluster
Output: Detection if the cluster is strong or weak

1: Initialize i = 0, cluster_link = 0, net_link = 0
2: while ( ! EOF)
3: Initialize j = 0
4: while ( ! null)
5: Store the values in multi – dimensional array
6: Increment j by 1
7: Increment i by 1
8: Calculate total_cost for each vertex using the multi – dimensional array
9: if (total_cost [vertex] >= limit)
10: edge [vertex] = 1
11: else
12: edge [vertex] = 0
13: Initialize count to 0
14: for m = 1 to n do
15: if edge [m] = 1
16: Increment count by 1
17: if (count) not equal to 0
18: cluster_link = count
19: else
20: cluster does not exist
21: Obtain max (neighbour_values) and store as degree of the respective cluster
22: Repeat steps 1 to 21 for all existing clusters in the considered network
23: From step 22, obtain net_link value
24: Use cluster_link, net_link and degree values to calculate Qm
25: Check the Qm value to see if the cluster is weak or strong
26: Stop

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International Journal of Computer Engineering and Technology (IJCET), ISSN 0976- 0976

In the algorithm the multi – dimensional array stores the values of tags, comments
and shares of that selected node. This is done in context with the social networking. These
values are used to calculate the cost or edge cost between two vertices in a network. The
o
existence of a weak or strong edge is determined by the limit value that is set. When an
edge exists as a strong edge between two vertices the edge count is incremented by one.
When the edge count for a cluster is null then no community structure can be
acquired out of it. But in existence of a valid edge count it is nothing but the number of
links existing with the chosen cluster and its value is stored in cluster_link. After the
th
acquisition of the cluster_link, we also require the degree of the cluster. This can be
acquired by choosing the maximum value out of all the neighbor values
(neighbour_values). The net_link refers to the number of links present in the entire
network. With the use of these values, the modularity factor can be calculated.
th

IV. CASE STUDY: SOCIAL NETWORKING (FACE BOOK)

The social networking site taken into consideration for this particular case study is
Facebook. In this, the authors have considered each member as a vertex of the network.
As given below in Fig.1, Facebook represents the undeterminable dynamic network as
1,
users tend to log in and log off at their interest. This is what provides the dynamicity of
the network. Under such circumstances the network siz is unknown.
size

Fig. 2: Randomized Network Structure
2

From that a random network is chosen, say students of a particular university.
Once this has been obtained, the next is the random selection of a cluster. In this cluster,
each student is a separate vertex. The aim is to characterize them based on their activities,
that is to say, detecting the communities under which the fall. Once the communities have

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been detected for a particular cluster, the same procedure is followed with other clusters
randomly chosen from the network. When all such communities from clusters have been
detected, the network as a whole can be viewed based on its detected communities. Given
below is a table, showing a set of sample data with respect to the considered scenario.

Table 1: Vertices associated with Random Selected Vertex from the Social
Networking site

NUMBER NUMBER
NUMBER TOTAL STRONG /
OF OF
VERTEX OF POSTS EDGE WEAK
PICTURES COMMENTS
SHARED COST EDGE
TAGGED GIVEN
Kethar
10 25 13 48 STRONG
Raghubalan

Sasikala
2 8 9 19 WEAK
Palani

Ankit Shah 13 5 8 26 STRONG

Hismath
21 18 2 41 STRONG
Begum

Dinesh
5 1 6 12 WEAK
Santhanam

In the above table, the sample data shows the working of the proposed algorithm
in determining the strength of the considered cluster of the network. From this, three edge
connections are determined to be strong while two of them are determined to be weak,
and are hence not considered for the community formation, as they exist as sole
communities with a single vertex.

V. CONCLUSION

The algorithm proposed above, as mentioned in the abstract, is only the first phase
towards achieving the objective of resolving the disadvantage of the multi objective
immune algorithm. The second phase of this algorithm is under process, and will be
submitted shortly. The second phase includes the proposal of an algorithm for the
removal or segregation of vertices into their corresponding communities. Also, currently
the tool being developed by the authors is for static purposes and work has been
commenced for enhancing it for dynamic purposes, wherein the communities are at
constant change depending upon the node activities.

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REFERENCES

Books

[1] M. E. J. Newman, Networks – An Introduction (Oxford)

Journal Papers

[2] Keehyung Kim, Ri McKay, and Byung – Ro Moon, Multiobjective Evolutionary
Algorithms for Dynamic Social Netowork Clustering, ACM 2010.
[3] Mao – Guo Gong, Ling – Jun Zhang, Jing Jing - Ma, and Li – Cheng Jiao,
Community Detection in Dynamic Social Networks based on Multiobjective Immune
Algorithm, Journal of Computer Science and Technology, May 2012.
[4] Jianbin Huang, Heli Sun, Yaguang Liu, Qinbao Song, and Tim Weninger, Towards
Online Multiresolution Community Detection in Large – Scale Networks, August 2011.
[5] M. E. J. Newman and M. Girvan, Finding and evaluating community structure in
networks, August 2003.
[6] M. E. J. Newman, Fast algorithm for detecting community structure in networks,
September 2003.
[7] C. O. Dorso and A. D. Menus, Community Detection in Networks, International
Journal of Bifurcation and Chaos, 2010.
[8] K. Sendil Kumar, K. S. Suganthi, C. Suchitra and S. Sharmili, An Analysis for the
Detection of Network Communities in Dynamic Environments, International Journal of
Applied Information Sciences, February 2013.

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Formulation of modularity factor for community detection applying

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