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TABLE OF CONTENTS

CHAPTERS Pg.No

Abstract iii

Acknowledgement ivTable of contents v

List of Figures

List of Tables

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1. Introduction 1

2. Problem Definition 4

3. Literature Survey

3.1 Complex networks definition

3.2 The Pattern

5

5

53.2.1 Average Path length 5

3.2.2 Degree Distribution 6

3.3 Generative Models 8

3.3.1 Erdos Renyi 9

3.3.2 Watts Strogatzz 10

3.3.3 Scale free 11

4. Project Requirement Definition 12

4.1 Data Set 12

5. System Requirement Specification 15

5.1 Functional Requirements 15

5.1.1 Software Requirement 15

5.1.2 Hardware Requirement 17

6. Gantt Chart 18

7. System Design 19

7.1 Local Centrality 19

7.2 Label Propagation 20

7.3 Elimination of Neighbors 21

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7.4 Random Walks 22

8. Detailed Design 23

8.1 Degree Centrality 23

8.2 Betweenness Centrality 24

8.3 Evaluation using Network-Coverage Algorithm 25

8.4 Proposed Methods 26

8.4.1 Local Centrality 26

8.4.2 Community Detection 27

8.4.3 Elimination of Neighbors 29

8.4.4 Random Walks 30

8.5 Comparative Analysis 329. Implementation 34

9.1 Local Centrality 34

9.2 Label Propagation 35

9.3 Random Walks 37

9.4 Elimination of Neighbors 38

10. Testing 39

10.1 Modules Tested 39

10.2 Data for testing 39

10.3 Results 40

10.3.1 Degree Centrality 41

10.3.2 Betweenness Centrality 41

10.3.3 Local Centrality 42

10.3.4 Label Propagation 42

10.3.5 Random Walks 43

10.3.6 Elimination by Neighbors 43

Conclusion 44

Further Enhancements 46

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Bibliography 47

LIST OF FIGURES

Fig.1.1 Twitter Social Network 2

Fig.3.1 Degree distribution of Citation Network 7

Fig.3.2 Degree distribution of Gnutella Network 8

Fig.3.1 Erdos-renyi graph with 10 nodes 10

Fig.3.2 Wattz-Strogatz graph with 10 nodes 11

Fig.3.3 Scale Free graph with 10 nodes 12

Fig.6.1 Gantt-Chart for Influential Analysis Project 18

Fig.7.1 Flow Chart for Local Centrality 19

Fig.7.2 Flow Chart for Label Propagation 20

Fig.7.3 Flow Chart for Elimination of Neighbors 21

Fig.7.4 Flow Chart for Random Walks 22

Fig.8.1 Degree Centrality 24

Fig.8.2 Betweenness Centrality 25

Fig.8.3 Community Detection 28

Fig.8.4 Random Walks 31

Fig.8.5 Comparative Analysis Of Proposed models 33

LIST OF TABLES

Table 3.1 Average Path length for real world graphs 6

Table 8.1 Results 32

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Table 10.1 Tabulation for Degree Centrality - Gnutella Graph 41

Table 10.2 Tabulation for Degree Centrality Arxiv HEP-PH 41

Table 10.3 Tabulation for Betweenness Centrality - Gnutella Graph 41

Table 10.4 Tabulation for Local Centrality - Gnutella Graph 42

Table 10.5 Tabulation for Local Centrality Arxiv HEP-PH 42

Table 10.6 Tabulation for Label Propagation - Gnutella Graph 42

Table 10.7 Tabulation for Random Walks- Gnutella Graph 43

Table 10.8 Tabulation for Elimination of Neighbors - Gnutella Graph 43

Table 10.9 Tabulation for Elimination by Neighbors Arxiv HEP-PH 43

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