Modularidade de Rede is a concept used in análise 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 ciência da computação, where systems can be represented as networks.
A modularidade é calculada comparando as conexões reais dentro da rede com as conexões esperadas em uma rede aleatória com a mesma distribuição de grau. A fórmula para a modularidade (Q) é:
Q = (1/2m) * Σ (Aij – (ki * kj) / 2m)
onde:
- Aij is the adjacency matrix of the network (1 if nodes i and j are connected, 0 otherwise).
- m é o número total de arestas na rede.
- ki e kj são os graus dos nós i e j.
Um valor de modularidade maior 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 aprendizado de máquina, and studying the spread of diseases or information through social networks.