Thesis: 2.5 Contribution to the literature
Our generalisation of the clustering coefficient represents an improvement of current network methods in that it helps capture the richness and complexity contained within the structure of weighted networks. By using the generalised coefficient, we can thus obtain a better understanding of the topology of weighted networks. The explanatory power of the existing clustering coefficient is limited due to the fact that it can only be applied to binary networks. This shortcoming has been overcome by another clustering measure, the local clustering coefficient. However, this measure is sensitive to the number of contacts a node has (Soffer and Vazquez, 2005) and its applicability is restricted to undirected networks (for a review, see Caldarelli, 2007). The non-local, or global, clustering coefficient that we focus on does not suffer from this sensitivity, and it is also defined for both undirected and directed networks. Thus, the generalisation is a step forward towards a more fine-grained analysis of weighted networks.
To exemplify the applicability of the generalised coefficient, we applied it to a number of empirical datasets ranging from friendship networks to neural ones. In every social network that we tested, we found that the generalised coefficient obtained a higher value than the binary one calculated when all positive ties were set to present. This signals that strong ties are more likely to occur inside triangles rather than outside. This result validates Granovetter’s (1973) assumption that weak ties are more likely to occur outside triangles than inside (Freeman, 1992). This assumption builds on Simmel’s (1950) work and refers to the fact that a person is less likely to have common contacts with “acquaintances” than with “friends”, and has implications for knowledge transfer. On the one hand, friends move in the same social circle and, therefore, their knowledge is likely to overlap (Coleman, 1988). On the other, acquaintances move in different social circles. This gives them access to novel pieces of information (Burt, 1992). By assessing whether strong ties occur within triangles, we provide a method for quantitatively testing this assumption.