clusteringcoefficiënt

Clusteringcoefficiënt is the Dutch variant of the clustering coefficient, a concept in graph theory and network science that measures the tendency of nodes to form tightly connected groups. The idea is to assess how close a node’s neighbors are to forming a clique. In practice, the term is often used interchangeably with coëfficiënt van clustering in Dutch literature, and with clustering coefficient in English texts. It applies primarily to undirected graphs, though weighted and directed versions exist.

Local clustering coefficient: For a node v with degree k_v, and e_v edges among its neighbors, the local clustering coefficient is C_v = (2 e_v) / (k_v (k_v − 1)) when k_v > 1, and 0 otherwise. It ranges from 0 to 1, with higher values indicating a greater likelihood that neighbors of v are connected to each other. A common global view is to take the average of C_v over all nodes, giving a mean local clustering coefficient.

Global clustering coefficient: The transitivity of a graph is defined as C = (3 times the number of triangles) divided by the number of connected triples of nodes. This global measure captures the overall tendency of the network to contain triangles. In many networks, the global coefficient is reported as the transitivity, while another approach is to report the average of local clustering coefficients; the two definitions may differ, especially in heterogeneous networks.

Variants and interpretation: For weighted networks, weighted clustering coefficients incorporate edge weights to reflect tie strength, with several formulations in the literature. For directed graphs, separate clustering coefficients can be defined for in- and out-neighborhoods. The clustering coefficient is used to study social networks, biological networks, and infrastructure systems, and it is sensitive to network size and degree distribution.