Structure and Evolution of Weighted Networks

In my thesis, I will outline and critically discuss some of the research projects on which I have been working during my Ph.D. programme. All my projects draw on, and extend, recent theoretical and methodological advances in network science.

Many social network measures can only be applied to networks in which ties are either present or absent. One of these measures is the clustering coefficient. The first project represents an attempt to overcome this shortcoming by proposing a generalisation of the clustering coefficient that is explicitly based on the weight of ties, and is therefore suitable to the analysis of weighted networks.

A second project investigates the nature of the interactions among prominent nodes in a network. To this end, a new general measure is proposed aimed at evaluating whether, and the extent to which, the strongest ties in the network occur among these nodes.

A third project explores the network growth mechanisms that underpin the evolution of social interaction over time. We utilised a regression framework to assess these mechanisms in an online social network. In particular, we investigate the effects of triadic closure, preferential attachment, reciprocity, homophily, focus constraints, and reinforcement on tie generation.

The aim of these projects is to contribute to a better understanding of the principles that govern the global organisation and functioning of networks.

In addition, a fourth project is devoted to the development of an open-source software programme that can deal with weighted and longitudinal networks, and incorporates the methods proposed in the other chapters. This project has the potential to provide researchers with a common platform on which new methodological advances easily can be made.

The thesis is available in a pdf-file (4.00mb) or in a html version (below). While the pdf-file is exactly as the thesis submitted, the html version contains a number of pointers to updated material.


1 Introduction
1.1 Weighted networks
1.2 Longitudinal networks
1.3 Projects and outline of thesis
1.4 Network datasets

2 Clustering in Weighted Networks
2.1 Clustering coefficient
2.2 Generalised clustering coefficient
2.3 Empirical tests
2.4 Directed networks
2.5 Contribution to the literature
2.6 Conclusion and discussion

3 Prominence and Control: The Weighted Rich-club Effect
3.1 The topological rich-club effect
3.2 The weighted rich-club effect
3.2.1 Null models
3.2.2 Significance of effect
3.3 Empirical tests
3.3.1 Club of the most connected nodes
3.3.2 Club of the most active nodes
3.3.3 Club of the nodes with the highest average weight
3.4 Contribution to the literature
3.5 Conclusion and discussion

4 Evolution of Networks
4.1 Network growth mechanisms
4.2 Cross-sectional binary networks
4.3 Longitudinal binary networks
4.4 Longitudinal weighted networks
4.5 Sensitivity to the number of control cases
4.6 Contribution to the literature
4.7 Conclusion and discussion

5 tnet: Software for Analysis of Weighted and Longitudinal networks
5.1 Data structures
5.2 Weighted network functions
5.3 Longitudinal network functions
5.4 Contribution to the literature
5.5 Conclusion and discussion

6 Concluding Remarks


Appendix A Presented and Published Papers

Appendix B Appendix to Prominence and Control: The Weighted Rich-club Effect
Appendix B.1 Directed Weight reshuffle when prominence is defined in terms of degree
Appendix B.2 Weighted rich-club effect in the Network Science collaboration network

Appendix C Source code of tnet 0.1.0
(This Appendix is not uploaded as it is outdated. See tnet’s website)

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