ネットワークのモジュール性 is a concept used in ネットワーク分析 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 コンピュータ科学, where systems can be represented as networks.
モジュラリティは、ネットワーク内の実際の接続と、同じ次数分布を持つランダムネットワーク内の予想される接続を比較することによって計算されます。モジュラリティ（Q）の式は次のとおりです：
Q = (1/2m) * Σ (Aij – (ki * kj) / 2m)
ただし：
- Aij is the adjacency matrix of the network (1 if nodes i and j are connected, 0 otherwise).
- mはネットワーク内のエッジの総数です。
- ki そして、kj はノードiとjの次数です。
0より大きいモジュラリティ値は 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 機械学習, and studying the spread of diseases or information through social networks.