Centrality measures and contagion on temporal networks Open Access

Chen, Isabel (2016)

Permanent URL: https://etd.library.emory.edu/concern/etds/p5547r73c?locale=en


The objective of this dissertation is to study the relationship between network-based centrality measures and epidemic outcome. Determining the key players in contagion processes can inform disease-prevention strategies. We analyze a time-stamped, person-to-person contact network based on human mobility movements within a busy, urban hospital. Movement patterns identified a small number of locations as hubs of activity. Linear algebraic techniques were used to compute a recently proposed temporal centrality measure applied to the empirical network; comparisons with traditional centrality measures were performed to determine if the inclusion of temporal information provides additional insights. Linear regression techniques were employed to describe the relationships between the quantities of interest. We find that while temporal centrality can at times identify key players not captured by traditional measures, it does not necessarily outperform non-temporal measures with respect to predicting epidemic outcome. Strategic removal of connections between highly central nodes resulted in an exponential decrease in the structural connectivity of the network, but this did not translate to a reduction in epidemic outcome. We conclude that contagion on temporal networks is extremely robust to changes in the network, and while network-based centrality can help to identify key players in an epidemic process, more work needs to be done to build an epidemic-containment strategy based on the information afforded by network-based analyses.

Table of Contents

1 Introduction. 1

1.1 Terminology. 9

2 Data. 14

2.1 Construction of the temporal network. 14

2.2 Temporal dynamics of contact network data. 19

2.2.1 Temporal dynamics of degree. 19

2.2.2 Temporal dynamics of pairwise interactions by type: SS, SP, PP. 21

2.3 Locations analysis. 21

2.3.1 Locations associated with interaction types: SS, SP, PP. 21

2.3.2 Most frequented locations. 23

2.3.3 Inactive locations. 23

2.3.4 Temporal dynamics of interactions at frequent locations. 26

3 Walk-based centrality measures. 29

3.1 Katz centrality. 30

3.2 Dynamic communicability. 33

3.2.1 Limit as α approaches zero. 37

3.2.2 Possible modications. 38

3.2.3 Data studied. 39

3.2.4 Relationship with the matrix exponential. 40

3.3 Classes of centrality measures. 42

4 Dynamic communicability applied to the data. 45

4.1 Robustness in the choice of α. 45

4.1.1 Computational Note. 46

4.1.2 BC and RC measures. 48

4.1.3 Comparison of node rankings. 50

4.1.4 Comparison of nodes in ranked order. 53

4.2 Dynamic communicability based on the matrix exponential. 53

4.3 Convergence to aggregate degree (AD). 54

4.4 Temporal dynamics of node ranking. 56

5 Interactions between top-ranked nodes. 60

5.1 Z analysis. 61

5.2 XY analysis. 62

6 Measures of virulence. 68

6.1 Stochastic Model. 70

6.2 Results. 71

7 Relationship between centrality and virulence. 74

7.1 Ranks analysis. 76

7.2 Regression analysis. 82

7.3 Interaction eects. 93

7.4 Prediction. 94

8 Targeted edge manipulation. 99

8.1 Epidemic measures. 100

8.2 Edge manipulation. 101

8.3 Effect of edge manipulation on dynamic total communicability (DTC). 105

8.4 Effect of edge manipulation on epidemic outcome. 110

8.5 Conclusion. 117

9 Conclusion. 118

Appendix A Partial lists of node rankings. 122

Appendix B Partial lists of nodes in ranked order. 123

Appendix C Pseudo-code for stochastic infection model. 124

Appendix D Mean EPI v centrality rankings. 128

Appendix E Max EPI v centrality rankings. 130

Appendix F NS-EPI v centrality rankings. 132

Appendix G Added-value of BC. 134

Appendix H Predictions. 136

Bibliography. 136

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