Tore Opsahl

Thesis: 3.5 Conclusion and discussion

Previous research has shown the importance of the nature of ties in a variety of network-based processes (Barrat et al., 2004; Coleman, 1988; Granovetter, 1973; Hansen, 1999; Krackhardt, 1992; Pastor-Satorras and Vespignani, 2004; Simmel, 1950; Uzzi, 1997). Drawing on measures for detecting topological rich-club orderings, we proposed a new general framework for the study of patterns of interactions among selected nodes in weighted networks. We tested this framework on three networks from the domains of transportation, scientific collaboration, and online communication. We extracted increasingly restrictive subsets of prominent nodes based on their degree, strength and average weight. Then, for each of these subsets, we examined whether the prominent nodes were more prone to direct their efforts towards one another than would be expected if the targets of these efforts were chosen randomly. Our results show that two of the networks analysed display non-trivial weighted rich-club effects among highly connected nodes. Conversely, when subsets were based on node strength and average weight, we found that prominent nodes tend to forge stronger ties with one another than randomly expected in all the networks.

The proposed method is widely applicable as it allows for an assessment of the control benefits of any subset of nodes. Prominence does not necessarily originate from network properties, such as node degree, strength, or average weight. To the extent that the nodes of a network can be ordered accordingly to a given property, our framework suggests several new ideas for future research. For example, how do performance, centrality, status, age, and size impact on the ability of nodes to control the strongest ties in a network? By providing insights into how prominent nodes, selected accordingly to different parameters, choose to direct their efforts towards one another, the proposed method represents a step towards furthering our understanding of the global organisation of complex networks.