## Posts tagged ‘complex networks’

Similar to the motivation of the global clustering coefficient that I proposed in Clustering in two-mode networks, the local clustering coefficient is biased if applied to a projection of a two-mode network. It is biased in the sense that the randomly expected value is not obtained on the projection of a random two-mode network. To overcome this methodological bias, I redefine the local clustering coefficient for two-mode networks. The new coefficient is a mix between the global clustering coefficient for two-mode networks and Barrat’s (2004) local coefficient for a weighted one-mode network. The coefficient is tested on Davis’ (1940) Southern Women dataset.

*January 6, 2010 at 6:29 pm*

The Online Social Network-dataset used in my Ph.D. thesis is now available on the Dataset-page. This network has also been described in Patterns and Dynamics of Users’ Behaviour and Interaction: Network Analysis of an Online Community and used in Prominence and control: The weighted rich-club effect and Clustering in weighted networks. The network originate from an online social network among students at University of California, Irvine. The edgelist includes the users that sent or received at least one message during that period (1,899). A total number of 59,835 online messages were sent among these over 20,296 directed ties.

The content of this post has been integrated in the

*tnet* manual, see

Datasets.

*November 10, 2009 at 5:46 pm*

This post explores the relationship between node degree and node strength in an online social network. In the online social network, heterogeneity in nodes’ average tie weight across different levels of degree had been reported. Although degree and average tie weight are significantly correlated, this post argues for the similarity of degree and node strength. In particular, high pair-wise correlation between degree and strength is found. In addition, power-law exponents of degree distributions and strength distribution are reported. The exponents are strikingly similar, in fact, they are almost identical.

Continue Reading *October 16, 2009 at 12:57 pm*

Many network dataset are by definition two-mode networks. Yet, few network measures can be directly applied to them. Therefore, two-mode networks are often projected onto one-mode networks by selecting a node set and linking two nodes if they were connected to common nodes in the two-mode network. This process has a major impact on the level of clustering in the network. If three or more nodes are connected to a common node in the two-mode network, the nodes form a fully-connected clique consisting of one or more triangles in the one-mode projection. Moreover, it produces a number of modeling issues. For example, even a one-mode projection of a random two-mode network with same number of nodes and ties will have a higher clustering coefficient than the randomly expected value. This post represents an attempt to overcome this issue by redefining the clustering coefficient so that it can be calculated directly on the two-mode structure. I illustrate the benefits of such an approach by applying it to two-mode networks from four different domains: event attendance, scientific collaboration, interlocking directorates, and online communication.

*September 11, 2009 at 12:00 am*

*tnet* is a package written in *R* that can calculate weighted social network measures. Almost all of the ideas posted on this blog are related to weighted networks as, I believe, taking into consideration tie weights enables us to uncover and study interesting network properties. Not only are few social network measures applicable to weighted networks, but there is also a lack of software programmes that can analyse this type of networks. In fact, there are no open-source programmes. This hinders the use and development of weighted measures. *tnet* represents a first step towards creating such a programme. Through this platform, weighted network measures can easily be applied, and new measures easily implemented and distributed.

The content of this post has been integrated in the

*tnet* manual, see

Software.

*June 12, 2009 at 12:00 am*

In this post, I extend the Weighted Rich-club Effect by suggesting and testing a different null model for the scientific collaboration network (Newman, 2001). This network is a two-mode network, which becomes an undirected one-mode network when projected. In the paper, we compared the observed weighted rich-club coefficient with the one found on random networks. The random networks were constructed by a null model defined for directed networks when prominence was based on node strength. Therefore, we created a directed network from the undirected scientific collaboration network by linking connected nodes with two directed ties that had the same weight. The null model consisted in reshuffling the tie weights attached to out-going ties for each node. However, this local reshuffling broke the weight symmetry of the two directed ties between connected nodes. The null model proposed in this post is based on the randomisation of the two-mode network before projecting it onto a one-mode network. By randomising before projecting, we are able to randomise a network while keeping the symmetry of weights.

*May 29, 2009 at 12:00 am*

I have now completed my Ph.D. at the School of Business and Management of Queen Mary College, University of London. My Ph.D. programme was defined around a number of projects, which drew on, and extended, recent theoretical and methodological advances in network science. The projects that were concerned with weighted networks and longitudinal networks were outlined and critically discussed in my thesis (Structure and Evolution of Weighted Networks). The entire thesis, except Appendix C which is outdated, is available on the Publication > Thesis-page.

**Acknowledgements**

The theme of this thesis is interdependence among elements. In fact, this thesis is not just a product of myself, but also of my interdependence with others. Without the support of a number of people, it would not have been possible to write. It is my pleasure to have the opportunity to express my gratitude to many of them here.

For my academic achievements, I would like to acknowledge the constant support from my supervisors. In particular, I thank Pietro Panzarasa for taking an active part of all the projects I have worked on. I have also had the pleasure to collaborate with people other than my supervisors. I worked with Vittoria Colizza and Jose J. Ramasco on the analysis and method presented in Chapter 2, Kathleen M. Carley on an empirical analysis of the online social network used throughout this thesis, and Martha J. Prevezer on a project related to knowledge transfer in emerging countries. In addition to these direct collaborations, I would also like to thank Filip Agneessens, Sinan Aral, Steve Borgatti, Ronald Burt, Mauro Faccioni Filho, Thomas Friemel, John Skvoretz, and Vanina Torlo for encouragement and helpful advice. In particular, I would like to thank Tom A. B. Snijders and Klaus Nielsen for insightful reading of this thesis and many productive remarks and suggestions. I have also received feedback on my work at a number of conferences and workshops. I would like to express my gratitude to the participants at these.

On a social note, I would like to thank John, Claudius, and my family for their continuing support. Without them I would have lost focus. My peers and the administrative staff have also been a great source of support. In particular, I would like to extend my acknowledgements to Mariusz Jarmuzek, Geraldine Marks, Roland Miller, Jenny Murphy, Cathrine Seierstad, Lorna Soar, Steven Telford, and Eshref Trushin.

*May 15, 2009 at 12:00 am*

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