Netzwerk-Modularität is a concept used in Netzwerkanalyse to quantify the strength of division of a network into modules (also called communities). A module is a group of nodes that are more densely connected to each other than to nodes outside the module. This concept is particularly applicable in various fields such as sociology, biology, and Informatik, where systems can be represented as networks.
Die Modularität wird berechnet, indem die tatsächlichen Verbindungen innerhalb des Netzwerks mit den erwarteten Verbindungen in einem zufälligen Netzwerk mit derselben Gradverteilung verglichen werden. Die Formel für die Modularität (Q) lautet:
Q = (1/2m) * Σ (Aij – (ki * kj) / 2m)
wobei:
- Aij is the adjacency matrix of the network (1 if nodes i and j are connected, 0 otherwise).
- m ist die Gesamtzahl der Kanten im Netzwerk.
- ki und kj sind die Grade der Knoten i und j.
Ein Modularitätswert größer als zero indicates that the network has a structure of communities, with higher values indicating more pronounced modularity. Conversely, a modularity close to zero suggests that the network’s connections are random or uniformly distributed.
Understanding network modularity has implications for various applications, including optimizing network design, enhancing the performance of algorithms in maschinellem Lernen, and studying the spread of diseases or information through social networks.