klustringskoefficient

Klustringskoefficient, often called clustering coefficient in English, is a measure in network analysis that quantifies the tendency of nodes to form tightly knit groups. It assesses how close a node’s neighbors are to forming a complete subgraph. For an undirected graph, the local clustering coefficient of a node i with degree k_i is defined as C_i = 2 e_i / (k_i (k_i − 1)) when k_i > 1, where e_i is the number of edges among the neighbors of i. A high value indicates that a node’s neighbors are highly interconnected.

Global clustering can be assessed in two common ways. One approach is to take the average of the local clustering coefficients across all nodes. A second approach is the transitivity measure, defined as C = 3 × number of triangles / number of connected triplets, which captures the overall level of clustering in the network independent of degree distribution.

There are extensions for weighted and directed networks. Weighted clustering coefficients incorporate edge weights to reflect the strength of ties, with several definitions proposed (for example by Onnela, Barrat, and others). In directed graphs, variants consider in-neighborhood and out-neighborhood connections, leading to multiple local and global versions.

Klustringskoefficient is commonly used to characterize network structure. Real-world networks frequently exhibit higher clustering than random graphs with the same degree distribution, which is a hallmark of community structure and the small-world phenomenon. It is applied in social networks, biological networks, collaboration networks, and technological networks to study transitivity, resilience, and cluster formation.