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Modern Physics Letters B
2050298 (20 pages)
© World Scientific Publishing Company
DOI: 10.1142/S021798492050298X
A novel method for destabilization of terrorist network
Saurabh Singh∗
Department of Computer Science and Engineering,
Jabalpur Engineering College, Jabalpur, Madhya Pradesh 482001, India
ssingh@jecjabalpur.ac.in
Shashi Kant Verma
Computer Science Department,
Govind Ballabh Pant Institute of Engineering and Technology,
Pauri Garhwal, Uttrakhand 246194, India
skverma.gbpec@rediffmail.com
Akhilesh Tiwari
Department of CSE & IT, Madhav Institute of Technology and Science,
Gwalior, Madhya Pradesh 474005, India
atiwari.mits@gmail.com
Received 19 February 2020
Revised 11 March 2020
Accepted 16 March 2020
Published 3 June 2020
Criminal network investigation is an ignited research area nowadays. There are several
types of criminal network. Terrorist network is one of them. Exploring terrorist network
is a demand of several investigating agencies. Different properties of network can be
better considered to probe network properly using multi criteria decision-making methods. Grey Relational Analysis (GRA) method is a structural technique for organizing
and analyzing complex decisions based on typical mathematics. This process can be
employed for analyzing available datasets and designing useful conclusions. If network
is explored and visualized, it can be destabilized efficiently. Identified members can be
studied and thus their future actions can be prevented. These generalized designs can
be used by government agencies for destabilization of terrorist group. This system is
especially useful for countries like India that face a constant threat from various group
of terrorists. This generalization can further be used to destabilize various criminal networks and their activities can be prevented. Thus, life and property of individuals can
be saved.
Keywords: Criminal networks; Covert networks; social networks; GRA method; betweenness centrality; closeness centrality; eigenvector centrality; PageRank centrality.
PACS Number(s): 89.65.-s, 89.75.-k, 89.20.Ff
∗ Corresponding
author.
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1. Introduction
To add to the miseries of uprising all around, Terrorism has become biggest threat
to the world. Terrorism is an illicit activity by a certain group of people, which
wind up taking life of many innocent citizens.1,2 Mass violence, acts of terrorism,
community trauma in various forms like shooting, bombing or by another type of
attack profoundly affects families and children.3 On deep analysis of this terrorism
attacks, it is found that people from various countries following an idea come up
together to form a large organization, which work on various layers of network and
these networks too are of various categories.4,5
The terrorist organization executes their plans by building a strong communication channel between its various members. They create a strong line of communication to ensure that the exchange of information and instruction is hidden from
outside world.6,7 The availability of the citizens data on the cheap communication
resources becomes a major source of information for the terrorists to plan all their
activities. Thus, a strong communication channel between terrorism organization
and leaking of citizen’s data results into a huge loss of life and property.8,9
To accomplish their dangerous thoughts, terrorists forms a terrorist network
so as to link people present in diverse geographical points to strategize their master plan ensuring a masked identity from the government.10,11 Internet and other
cellular networks form an active communicational network, supporting enormous
number of devices such as mobile and other intelligent communication devices acting as stationary nodes.
The concept of terrorist network is generally amalgamated with Covert network.12 A Covert network is a social network that involves influential miscreants
who conceal their identity. The sharing of events among the representatives of the
network is done in a very secretive manner. Rather, the Covert channel cannot be
controlled or detected by the security mechanism that underlines a secure analogy
between the Covert network and Terrorist network.13 Terrorist Organization have
been moving ahead toward a network structure goal of more security through social
and geographical decentralization.
The intra-terrorist network works in highly conceivable manner to stay isolated
from data breaches. To further this cause, the member protects their identity that
may be done by the anonymous name, which means you are not leaving any traces
of who you are. Anonymity aids to hide the strategies and mastermind from the
investigating authorities. Many terrorist organizations get financial aids from various other cooperate organization, removing this cooperate organization will affect
the whole terrorist network.14
Terrorist organizations are composed of quasi-independent cell rather than partitioning them in discrete levels. In sense, the terrorist network is built so strategically
that gives them profound assurance of not getting captured by anyone. Hence, they
preferably construct a decentralized network where individual importance depends
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A novel method for destabilization of terrorist network
on the information that can be extracted from the person not necessarily the person
being a terrorist. The job done in this network is always in prone to be caught by
the authorities, because one suspect under their arms can shatter the full-fledged
network. Hence, determination of structure (hierarchy) seems irrelevant. If once
the network gets enfeebled, it becomes far easy to identify the people working in
difficult field, which further cause consequences to the whole network. The threat
of terrorist network is wreaking havoc in the society. Determination of the terrorist
network helps us to avoid the circumstances of the upcoming calamity. This will
maintain the peace and tranquility of the surroundings.
The global terror network that led to attack of 9/11 has triggered the major
initiatives of the United States to combat terrorism.15 This has caused a massive explosion that resulted in burning debris all over the surrounding and onto
the street below. This series of airline hijacking and suicidal attacks caused extensive death and destination. By data analysis, it was found out that terrorists
were in close contacts and used to communicate in encrypted language. Similarly,
the 4-day militant attack of 26/11 in Mumbai (India) leads to killing of many
innocents. The terrorist usually makes use of Internet to collect information regarding the place to be attacked, traveling tickets, to steal social security numbers,
etc. Terrorists have tried every possible way to remain undetected from Internet.
For instance, they have sent a graphic file or a digital song file, which has encrypted message hidden over it. Hence, the wide terrorist network becomes tough
to tackle.
In the series of well-devised plans to ruin the particular place, the attack of 7/7
London bombing incident, which includes four suicide bombers with rucksacks full
of explosives attached central London, resulted in loss of many and affected the
survival of all who lives in surrounding places. It has also been regarded as one
of the worst attacks. Moreover, there has been many catastrophic events, which
depredate the freedom of people. The use of intentional violence for religious and
political purposes has gained mainstream popularity, especially it is used to gain
much media coverage. Over the previous decades, the average deaths counted annually is approximately 21,000. However, there can be year-to-year variability. Though
terrorist attacks are usually regionally focused, but statistics reveal that no part
of the country has remained untouched from the fright of terrorist attack. The list
of massacre’s are uncountable and fatalities took beneath are even more. Initially,
to put this violence to an end, terrorist network has played a requisite role, which
helps in determining the correlation of the attackers involved. Communication has
been a biggest source of dataset, which unwrap the ideology of each individual.
So, Terrorist Network has been developed with many features, which puts on a
strenuous challenge before us to shatter the network.
In this fleet footed world, computers have emerged as a life-changing tool by
increasing productivity of an organization, providing its accurate and powerful processing and computational capabilities. Since calculations and processing of large
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S. Singh et al.
amount of data are required in tracing the terrorist and criminal movements, thus
computer shows its dominance in this field too through application of its computational and mathematical concepts to analyze the terrorist network.
Pictorial analysis is always easier to grasp rather than numerical analysis of any
dataset. Graph is such an illustration that represents data pictorially. Thus, graph
theory is of great importance not only in mathematics, but also in Computer Science. Graphs are mathematical structure that exhibit relationship between objects.
It is a framework that consists of two components: vertices and edges. Vertices
represent objects, on the other hand edges symbolizes relationship between those
objects.16 Edges may or may not have a particular direction and weight to determine their significance in graph.17
Various methods have been examined under multi-criteria decision-making
(MCDM), which evaluates each method and do a critical comparison with respect
to maintenance management. MCDM method includes Analytic Hierarchy Process
(AHP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS),
Elimination and Choice Expressing Reality (ELECTRE) and Grey Relational Analysis (GRA). Out of all the four methods, GRA is one of the best methods that measures the degree of grey relation. It provides technique for determination of good
and appropriate solution to real-world problems inspite of attempting for best solution. It is used to bring solution of the uncertainty problems under the discrete
data. The more positive the ideal solution is, the more will be its degree of grey
relation and vice versa. Also, GRA method easily captures the dynamic objective
features of different factors, which helps to save lot of time and cost. Hence, GRA
method helps in management to make vital decision under Business environment.
2. Literature Survey
With the ceaseless sustained rise in terrorism, varied organizations are obliged to
work to elucidate this bemusing network. Terrorist network analysis has been eminence round the clock, especially since 9/11 attack. Inflating such an excruciating
act has placed the counterpart at a frantic situation, where quick pedantry and
expansion in techniques is the only option to keep out of harm’s way. Thinkers
are working around the clock to fight this formidable strength. Some of these approaches are chronicled in this section.
To accomplish a summarizing view of such a network for analysis, unification of
data is required. But due to different organizations owning different social network
data, this gets onerous cause individual body inhibiting sensitive data to maintain
privacy sphere. Tang and Yang18 deals with this issue by suggesting a generalization
algorithm, which gives room to a body to keep open only that part of the data whose
sharing does not affect the privacy and sharing it so as to assist creating integrated
global network that can be available to undertake analysis. This is achieved by
creating subgraphs and then generalizing these subgraphs to let them integrate to
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A novel method for destabilization of terrorist network
modulate social network. These subgraphs are insensitive, but relevant data that
both safeguards privacy and enables integration of global social data.
Li, Sun, Guo and Li19 used combination of varied techniques and methodology
to hold out the key individuals in terrorism such as Social Network Analysis (SNA)
and Fuzzy Analytical Network Process (FANP). The rating of individuals is done
by broaching measures from total degree, betweenness, closeness, which is further
embedded in a devised indexing system of network computer by ORA. Further, the
methods of artificial judgment and fuzzy science is applied to the method laterally explicated. It is ascertained a good method to meet the circumstances, where
the information mustered may be uncertain. This model was referred to embassy
bombing of Kenya and Tanzania, where it proved luminary in detecting the key
elements of terrorism.
Dawoud, Alhajj and Rokne20 suggest that the aim of this peculiar paper is to
indicate that understanding of the basic hierarchical structure of such excruciating
network is key in determining the strength and weakness of a group or organization.
This helps exceedingly in determining capabilities of such networks. Previously, this
methodology was applied to legal organizations that has got most of its information
transparent. But the work extends when this comes to an illegitimate constraint,
where the network hierarchy is hidden. The role of such methodology comes into
play when particular nodes of such network hide their identity, rule and organizational structure. Determining the degree of network and their strength is what this
algorithm helps with.
Ozgul, Erdem and Bowerman21 on the other hand, fabricated a model to prognosticate and detect the particulars behind the unsolved cases. The model is called
the Crime Prediction Model (CPM). The model tries placing few solved and unsolved cases in the same clusters based on the basis of the time, location, motive
of the crime, etc. These clusters are referred to attain classification module. If unsolved and solved cases from a particular cluster is found adequately similar, the
same group or organization as a solved case is regarded responsible or somehow
associated with the unsolved crimes.
The Internet is flourishing at the steepest way than anything has ever expanded.22 Capitalizing the same, dark web has sheltered all the anti-humanities
around. Terrorist networks also have set their empire to commute their messages.
The establishment of a system to analyze dark web can be worth devising for
counter-terrorism and avoiding menaces. Sachan23 suggested a dark web analysis
method that piles up message data from the dark web forum and tables are created
so as to list message posters and are categories on the basis of their activity level like
exchanging ideology, spreading propaganda and recruiting new members. Joining
dots from these dark web forums can help getting to the core of such networks.
A network is connections between various people that provide them convince
to communicate. Likewise, terrorist connects with the help of terrorist network.
Their networks have a complex design to ensure masked identity of the terrorist.
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Unlike other, networks too have links and nodes. Each paper of the network help
in tracing the people involved. The links in terrorist network provide much important information regarding their organization as explained by Wiil, Gniadek and
Memon.24
Unlike any other organization, terrorist organization too always have a backup.
If some terrorist is removed from the network, definitely other will take their place.
We can analyze that which person is going to be replaced and by whom. Spenzzano
and Mannes25 worked on algorithm for PSP, which includes all the requirement in
the person for replacing the existing one.
Visual analysis of social media data can be visually analyzed by firstly selecting
the relevant data, then processing it and fixing the geo-location coordinate.26 Then
data mining is done and various patterns are analyzed, and finally the social media
data can be visualized as explained by Schreck and Keim.27 This method can be
applied to terrorist network and data to visualize it and to make the analysis easy.
The analysis is done on various crime-related networks and communities are
studied using random walk-based algorithm by Alzahrani and Horadam.28 These
identifications of various criminal communities can help to get many important
information, and help in finding the terrorist coterie.
Every organization need a financial support to run smoothly similar as in the
case of terrorist organization. The analysis on the source of funding of terrorist
organization will help us to get up them. Thus, various data-mining and social
networking can be applied and pattern of terrorist financial transaction is studied
to get more information regarding the terrorist network by Sakharova.29
Ozgul and Atzenbeck,30 developed crime analogy-based similarly measures
(COSMs). It aims to detection of criminal by the demography features, i.e. origins
and ethic. Basically, COSM is used for data study of Istanbul terrorist group. It
can be applicable to the similar crime networks to build a dataset. Hence, detection
of criminals can be done.
Especially for Chinese economy,31 Yuan and Zhang worked on GRA method
by using the weight entropy. With the motive of investigating the relative data on
electronic commerce, GRA method has been introduced. The “degree of incidence”
is the term, which is to be obtained for different datasets and result is verified.
To enhance the quality and quantity of product, the maintenance perspective has
been implemented in the MCDM.32 The paper includes different available methods
and has compared on the basis of accuracy, consistency, problem structure, concept, etc. Hence, accurate results can be obtained with very minimal efforts and
investments.
Comprises of different MCDM methods and a comparative study have been done
among the available alternatives. Differentiation has been done based on various
parameters that are strengths and weakness. It simply tells about the importance
of MCDM in solving the complex real problems.33
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A novel method for destabilization of terrorist network
The terrific incident of 26/11 has tragic outcomes, which affected the lives of
many.34 This paper has analyzed the terror attack based on the mathematical technique, i.e. SNA. This includes data tracing of telephonic communications between
the attackers who were a part of the terrorist attack. The communication gives the
idea of central node, which refers to the master planner of the attack and also tells
about the interconnection of different persons involved.
3. Methodology
Laterally, explicated GRA method is brought into effective actions to discern the
most noteworthy node in foreshortening terrorist network. The screened node after
availing GRA is further taken into consideration by the authorities to take felicitous
action.
Thereby designating nodes based on criteria, particularly for this paper graph,
properties such as betweenness centrality, closeness centrality, eigen value centrality
and page rank centrality are taken into account.
The Betweenness Centrality attribute of a graph comprehends the foremost
node. The node with maximum Betweenness centrality is the one that functions as
bridge between two specific nodes and shortest path between them for the maximum
number of times. This particular node can be earmarked to warp the terrorist
network as this node bears maximum control over network flow.
For instance, in Fig. 1, every shortest path bridging node 1 and node 6 confronts
node 5, thereby ascertaining maximum Betweenness Centrality. Closeness Centrality defines how close a specific node is to all the other nodes. It can be calculated
as the reciprocal of the sum of distance between a node and all other nodes in the
graph.35 The more centralized a node is, the more it is connected to the rest of the
nodes and is responsible for data sharing. Thus, it can be a destination for agencies
to target.
In Fig. 2, node 1 is clearly the centermost, as it is close to all the other nodes in
the graph. Eigenvalue Centrality determines the influence of a node in a particular
network compared to other nodes. Relative scores are assigned to the nodes on the
term that a node connects more high-scoring nodes.
Fig. 1.
Betweenness Centrality.
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S. Singh et al.
Fig. 2.
Closeness Centrality.
Fig. 3.
Eigenvalue Centrality.
In Fig. 3, although node 2 bridges to node 1 only but ascertaining maximum
Eigenvalue Centrality as node 2 is in turn connected to many nodes.
Those individuals or organizations connecting either too many or are isolated
otherwise are scored less. Although, the nodes in connection with such nodes that
have many connections themselves are scored high.
PageRank Centrality gives preferences to a node on the basis of incoming neighbors. The nodes are well normalized and are interpreted accordingly, predicting the
transition from one node to other as shown in Fig. 4.
Fig. 4.
PageRank Centrality.
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A novel method for destabilization of terrorist network
Fig. 5.
Framework of GRA.
The framework of the GRA method is shown in Fig. 5.
The execution steps are as follows:
• Step 1: Normalization of Matrix: Matrix is normalized such that each cell acquires respective parameter.
• Step 2: Weighting the Normalized Matrix: A weighted normalization matrix is
obtained from the specified weights by multiplication of weights with respective
cell of normalized value.
• Step 3: Grey Relational Generating:
Case (a): If the expectancy is the higher-the-better
x∗ (k) =
x0i (k) − min x0i (k)
max x0i (k) − min x0i (k)
(1)
Case (b): If the expectancy is the lower-the-better
x∗ (k) =
max x0i (k) − x0i (k)
max x0i (k) − min x0i (k)
where
i = 1, . . . , m; k = 1, . . . , n.
m = number of criteria
n = number of alternatives
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(2)
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Algorithm 1. Algorithm to de-stabilize the network.
Input: Terrorist Network Graph G(V, E), List of selected criteria – between
centrality, closeness centrality, Pagerank centrality, Eigenvector centrality
Output: Ranking of most significant node
• Step 4: Find the Grey relational Coefficient:
ϕi (k) =
∆ min +θ∆ max
∆0,i (k) + θ∆ max
(3)
∆0,i (k) is the deviation sequence,
• Step 5: Find the Grey relational Grade:
n
1X
γi =
ϕi(k)
n
(4)
k=1
• Step 6: Calculate the Rank of each alternative: Sort the Grey relational grade in
descending order and assign rank accordingly from 1 to m.
3.1. Pseudocode
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
initialize input data
input data[m][n]
for i = 0 to n
min[i]= min(input data[0:m][i])
max[i]= max(input data[0:m][i])
for i = 0 to n
for j = 0 to m
norm data[i][j]= (input data[i][j]-min[i])/(max[i]-min[i])
for i = 0 to n
min[i]= min(input data[0:m][i])
max[i]= max(input data[0:m][i])
for i = 0 to n
for j = 0 to m
dev seq[i][j]=max[i]-norm data[i][j]
for i = 0 to n
min[i]= min(input data[0:m][i])
max[i]= max(input data[0:m][i])
for i = 0 to n
for j = 0 to m
GRC[i][j]=(min[i]+(0.5)*max[i])/ (dev seq[i][j]+(0.5)*max[i])
Find Grey relational grade
for i = 0 to n
for j = 0 to m
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• GRG[i]=(1/n)*sum(GRC[i])
• Find Rank
• Rank=sort(GRG)
3.2. Time complexity analysis
3.2.1. Generating of Grey Relation
•
•
•
•
•
•
•
•
•
Let n will be the no. of criteria and m will be no. of alternatives.
For finding min for each criteria = m1
For finding max for each criteria = m2
So, for n criteria = (m1+m2)n = 2mn
As size of m1 = m2.
Time to minus = C1
Time to divide = C2
For m alternatives and n Criteria = mn(C1 + C2)
Time Complexity for 1st step = 2mn + nm(C1+C2) = O(mn)
3.2.2. Finding Grey Relation Coefficient
•
•
•
•
•
•
•
•
•
•
For finding min for each criteria = m1
For finding max for each criteria = m2
So, for n criteria total time complexity = (m1+m2)n = 2mn
As size of m1 = m2.
Time to minus = C1
For m criteria and n alternatives = (mn)C1
Time for addition = C2
Time to divide = C3
For m alternatives and n criteria = mn(C2 + C3)
Time Complexity for 2nd step = 2mn + mnC1 + mn(C2+C3) = O(mn)
3.2.3. Finding Grade of Grey Relation
•
•
•
•
•
Time to sum = C1
For n criteria = nC1
Time to divide = C2
For m alternatives = m(nC1 + C2)
Time Complexity for 3rd step = m(nC1 + C2) = O(mn)
3.2.4. Final Ranking
• Time to sort m alternatives = m(logm)
• Time Complexity for 4th step = O(mlogm)
Time Complexity from 1st step to 4th step = O(mn)
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4. Results and Simulation
This work includes terrorist network dataset of 26/11 attacks in Mumbai25 to visualize execution of GRA method. It is a binary dataset, showing link between
two terrorists. Government of India report36 had been analyzed properly to collect
the associations among terrorists. Binary dataset that is generated after careful
analysis of Ref. 36 is used in Ref. 34. Final dataset is shown as adjacency matrix
in Appendix A. With the help of ORALITE software, the data are envisioned a
network (Fig. 6). For better readability, some alias (reference names) have been
created, which is defined in Table 1.
Out of various centrality measures calculated using ORA-LITE software, only
four (Betweenness centrality, Closeness centrality, Page rank centrality and Eigen
vector centrality) centralities are used.
Fig. 6.
Network image of 26/11 terrorist attacks in Mumbai.
Table 1. All certain terrorists
mapped in the following fashion.
A
B
C
D
E
F
G
H
I
J
K
L
M
are
Abu Kaahfa
Wassi
Zarar
Hafiz Arshad
Javed
Abu Shoaib
Abu Umer
Abdul Rehman
Fahadullah
Baba Imran
Nasir
Ismail Khan
Ajmal Amir Kasab
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Table 2.
Centralities calculated using ORA-LITE software.
Name
Betweenness
Centrality
Closeness
Centrality
PageRank
Centrality
Eigenvector
Centrality
A
B
C
D
E
F
G
H
I
J
K
L
M
0.136
0.503
0.08
0.003
0
0
0.003
0
0.072
0
0
0
0
0.279
0.308
0.279
0.267
0.261
0.267
0.267
0.24
0.245
0.25
0.25
0.083
0.083
0.087
0.187
0.076
0.089
0.084
0.069
0.089
0.032
0.071
0.031
0.031
0.077
0.077
0.246
0.612
0.23
0.469
0.469
0.469
0.469
0.088
0.131
0.142
0.142
0.154
0.154
Table 3.
Normalized table.
Name
Betweenness
Centrality
Closeness
Centrality
PageRank
Centrality
Eigenvector
Centrality
A
B
C
D
E
F
G
H
I
J
K
L
M
0.270378
1
0.159046
0.005964
0
0
0.005964
0
0.143141
0
0
0
0
0.871111
1
0.871111
0.817778
0.791111
0.817778
0.817778
0.697778
0.72
0.742222
0.742222
0
0
0.358974
1
0.288462
0.371795
0.339744
0.24359
0.371795
0.00641
0.25641
0
0
0.294872
0.294872
0.301527
1
0.270992
0.727099
0.727099
0.727099
0.727099
0
0.082061
0.103053
0.103053
0.125954
0.125954
The four columns indicate the parameters to be considered to make the decision.
Values for four columns have been taken from the report of ORALITE software as
shown in Table 2.
The method of GRA involves following steps:
• Step 1: Normalization of matrix
In this step, column values are normalized on the scale of 0 to 1. So, the resultant
table is shown as Table 3.
• Step 2: Weighting the normalized matrix
In this step, each column is multiplied by its weights. Weights are value that
determines the importance of the corresponding parameter in decision-making.
Weight assignment is shown in Table 4. After assignment of each criterion, resultant table is shown as Table 5.
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Table 4.
Weights for each parameter.
Centrality
Closeness Centrality
PageRank Centrality
Eigenvector Centrality
Sum
Table 5.
0.3
0.3
0.2
0.2
01
Weighted table.
Name
Betweenness
Centrality
Closeness
Centrality
PageRank
Centrality
Eigenvector
Centrality
A
B
C
D
E
F
G
H
I
J
K
L
M
0.081113
0.3
0.047714
0.001789
0
0
0.001789
0
0.042942
0
0
0
0
0.261333
0.3
0.261333
0.245333
0.237333
0.245333
0.245333
0.209333
0.216
0.222667
0.222667
0
0
0.071795
0.2
0.057692
0.074359
0.067949
0.048718
0.074359
0.001282
0.051282
0
0
0.058974
0.058974
0.060305
0.2
0.054198
0.14542
0.14542
0.14542
0.14542
0
0.016412
0.020611
0.020611
0.025191
0.025191
Table 6.
Deviation sequence.
Name
Betweenness
Centrality
Closeness
Centrality
PageRank
Centrality
Eigenvector
Centrality
A
B
C
D
E
F
G
H
I
J
K
L
M
0.918887
0.7
0.952286
0.998211
1
1
0.998211
1
0.957058
1
1
1
1
0.738667
0.7
0.738667
0.754667
0.762667
0.754667
0.754667
0.790667
0.784
0.777333
0.777333
1
1
0.928205
0.8
0.942308
0.925641
0.932051
0.951282
0.925641
0.998718
0.948718
1
1
0.941026
0.941026
0.939695
0.8
0.945802
0.85458
0.85458
0.85458
0.85458
1
0.983588
0.979389
0.979389
0.974809
0.974809
• Step 3: Generation of Grey relation
In this step, deviation sequence table is calculated. All the column values are
subtracted by maximum value in the same column. In our case, the normalized
table has maximum value 1 for all the columns. Hence, Deviation Sequence in
calculated by subtracting all values by 1.
Deviation Seq. = X max - X
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Table 7.
Grey Relation Coefficient.
Name
Betweenness
Centrality
Closeness
Centrality
PageRank
Centrality
Eigenvector
Eigenvector
A
B
C
D
E
F
G
H
I
J
K
L
M
0.352389
0.416667
0.344285
0.333731
0.333333
0.333333
0.333731
0.333333
0.343157
0.333333
0.333333
0.333333
0.333333
0.40366
0.416667
0.40366
0.398512
0.395987
0.398512
0.398512
0.387397
0.389408
0.391441
0.391441
0.333333
0.333333
0.35009
0.384615
0.346667
0.350719
0.34915
0.344523
0.350719
0.333618
0.345133
0.333333
0.333333
0.346975
0.346975
0.347296
0.384615
0.345829
0.369118
0.369118
0.369118
0.369118
0.333333
0.337021
0.337977
0.337977
0.339027
0.339027
Table 8.
Grade of Grey Relation.
Name
Grey Relation Grade
A
B
C
D
E
F
G
H
I
J
K
L
M
0.363359
0.400641
0.36011
0.36302
0.361897
0.361372
0.36302
0.34692
0.35368
0.349021
0.349021
0.338167
0.338167
Here, X = original value, X max = maximum value in the corresponding column.
Then resultant table is Table 6.
• Step 4: Finding Coefficient of Grey Relation
In this step, a grey relation coefficient is calculated for each value by this formula:
Φi (k) =
∆min + Θ∆max
∆0,i (k) + Θ∆max
(5)
Here, ∆min = 0, ∆max = 1, ∆0,i (k), and Θ = Identification Coefficient (It is
assumed as 0.5). Then resultant table is visualized as Table 7.
• Step 5: Finding Grade of Grey Relation
In this step, the average value of all the columns in Grey Relation Coefficient
table is calculated for each row. This value is called Grey Relation Grade as
shown in Table 8.
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Table 9.
Sorted Grade of Grey Relation.
Name
Grey Relation Grade (sorted)
Wassi
Abu Kaahfa
Abu Umer
Hafiz Arshad
Javed
Abu Shoaib
Zarar
Fahadullah
Baba Imran
Nasir
Abdul Rehman
Ajmal Amir Kasab
Ismail Khan
0.4006410256410256
0.36335860977911794
0.3630202823582347
0.3630202823582347
0.36189705769356173
0.36137164599960303
0.36011004648074507
0.35367975049476724
0.3490211159730346
0.3490211159730346
0.3469204595531487
0.33816716768712746
0.33816716768712746
Table 10.
Name
Final selection of alternatives.
Grey Relation Grade (top five)
Wassi
Abu Kaahfa
Abu Umer
Hafiz Arshad
Javed
0.4006410256410256
0.36335860977911794
0.3630202823582347
0.3630202823582347
0.36189705769356173
• Step 6: Final selection of alternative to destabilize the network
To get the final ranking, all the rows of Table 8 are sorted in ascending order of
Grey Relation Grade. Top elements in this table are the most important according
to GRA Algorithm as shown in Table 9. Then, top five alternatives are selected
to destabilize the terrorist network as shown in Table 10.
Fig. 7.
Visualization of Grey relation grade.
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A novel method for destabilization of terrorist network
Fig. 8.
Fig. 9.
Visualization of sorted alternatives.
Visualization of final selection of alternatives.
Grey relation grade of all the alternatives is envisioned in Fig. 7.
On the basis of grade alternatives are sorted and displayed in Fig. 8.
Top five alternatives are selected to destabilize the terrorist network as shown
in Fig. 9. Removal of these nodes (alternatives) would destabilize the network as
these are most influencing nodes.
2050298-17
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5. Conclusion and Future Work
The GRA model is very productive to find deserving alternative out of given alternatives. Power of GRA method is ease of use. Also, GRA method requires less
computational effort, so it is speedy in nature.
Data of 26/11 attacks of Mumbai,34 India, are analyzed here and findings are
found very useful. Fetched results are very informative and it can better explore
the network up to some level. Results showing Wassi, Abu Kaahfa, Abu Umer,
Hafiz Arshad and Javed are most important nodes and confirmed by Ref.36 Present
work is very satisfying to find loopholes of criminal network and to destabilize
further.
However, GRA method is working well in criminal investigation, but to pinpoint
process of destabilization of the network, some supporting optimization methods
are required. Scalability of present method should also be tested.
After going through various literatures and present work, it can be concluded
that destabilization of network is being done using one method only. Approach of
multiple methods is required. Multiple methods can be applied simultaneously or
in pipeline fashion. So how to apply approach is also a question of further research.
Work presented here is useful for criminal network investigation, but might be the
basis of investigation of counterfeit information that is spreading on social networks.
Investigation of counterfeit message and getting source of it is a big crisis in the
coming days.
Appendix A
26/11 Mumbai Attacks Dataset
A.
H.
A.
A.
A.
B.
I.
A. A.
Kaahfa Wassi Zarar Arshad Javed Shoaib Umer Rehman Fahadullah Imran Nasir Khan Kasab
A. Kaahfa
0
1
1
0
0
0
0
0
0
0
0
0
0
Wassi
1
0
1
1
0
0
1
0
0
1
1
0
0
Zarar
1
1
0
0
0
0
0
0
0
0
0
0
0
H. Arshad
0
1
0
0
1
1
1
0
0
0
0
0
0
Javed
0
0
0
1
0
0
1
0
0
0
0
0
0
A. Shoaib
0
0
0
1
1
0
1
0
0
0
0
0
0
A. Umer
1
1
0
1
1
1
0
0
0
0
0
0
0
A. Rehman
0
0
0
0
0
0
0
0
1
0
0
0
0
B. Imran
0
0
1
0
0
0
0
1
0
0
0
0
0
Fahadullah
0
1
0
0
0
0
0
0
0
0
0
0
0
Nasir
0
1
0
0
0
0
0
0
0
0
0
0
0
I. Khan
0
0
0
0
0
0
0
0
0
0
0
0
1
A. A. Kasab
0
0
0
0
0
0
0
0
0
0
0
1
0
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