Modularidad de red is a concept used in análisis de redes 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 ciencias de la computación, where systems can be represented as networks.
La modularidad se calcula comparando las conexiones reales dentro de la red con las conexiones esperadas en una red aleatoria con la misma distribución de grados. La fórmula para la modularidad (Q) es:
Q = (1/2m) * Σ (Aij – (ki * kj) / 2m)
donde:
- Aij is the adjacency matrix of the network (1 if nodes i and j are connected, 0 otherwise).
- m es el número total de aristas en la red.
- ki y kj son los grados de los nodos i y j.
Un valor de modularidad mayor que 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 aprendizaje automático, and studying the spread of diseases or information through social networks.