Klasterfaktor

Klasterfaktor is a term used in graph theory and network analysis to describe the degree to which nodes in a network tend to cluster together. It quantifies the tendency of a node's neighbors to also be neighbors of each other. In simpler terms, it measures how interconnected a node's immediate connections are. A high klasterfaktor indicates that if two nodes are connected to the same central node, they are also likely to be connected to each other. Conversely, a low klasterfaktor suggests that connections are more spread out, and neighbors of a node are less likely to be directly connected.

The klasterfaktor is often calculated for individual nodes within a network, providing a measure of local clustering. It can also be averaged across all nodes in a network to represent the overall clustering tendency of the entire graph. This metric is particularly useful in understanding the structure of complex systems, such as social networks, biological networks, or communication networks. For example, in social networks, a high klasterfaktor might indicate the presence of tight-knit communities or cliques, where individuals tend to know people who also know each other. In biological networks, it could highlight functional modules or protein complexes.

The calculation typically involves comparing the number of actual connections between a node's neighbors to the total possible number of connections between those neighbors. A value of 1 signifies perfect clustering, where all neighbors of a node are connected to each other. A value of 0 indicates no clustering, meaning none of a node's neighbors are connected to each other. The klasterfaktor provides a quantitative way to describe the "cliquishness" of a network.