Research Institute of Electrical Communication, Tohoku University, Sendai, Miyagi 980-8577, Japan.
WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai, Miyagi 980-8577, Japan.
Chaos. 2019 Jan;29(1):013142. doi: 10.1063/1.5044689.
We considered a modular network with a binomial degree distribution and related the analytical relationships of the network properties (modularity, average clustering coefficient, and small-worldness) with structural parameters that define the network, i.e., number of nodes, number of modules, average node degree, and ratio of intra-modular to total connections. Even though modular networks are universally found in real-world systems and are consequently of broad interest in complex network science, the relationship between network properties and structural parameters has not yet been formulated. Here, we show that a series of equations for predicting the network properties can be related using a mean-field connectivity matrix that is defined on the basis of the structural parameters in the network generation algorithm. The theoretical results are then compared with values calculated numerically using the original connectivity matrix and are found to agree well, except when the connections between modules are sparse. Representation of the structure of the network using simple parameters is expected to be conducive for elucidating the structure-dynamics relationship.
我们考虑了一个具有二项式度分布的模块化网络，并将网络属性（模块度、平均聚类系数和小世界性）的分析关系与定义网络的结构参数（节点数、模块数、平均节点度和模块内连接与总连接的比例）联系起来。尽管模块化网络在现实世界的系统中普遍存在，因此在复杂网络科学中具有广泛的兴趣，但网络属性和结构参数之间的关系尚未得到制定。在这里，我们表明，可以使用基于网络生成算法中的结构参数定义的平均场连接矩阵，将一系列用于预测网络属性的方程联系起来。然后，将理论结果与使用原始连接矩阵数值计算的值进行比较，发现除了模块之间的连接稀疏时，结果吻合得很好。使用简单参数表示网络结构，有望有助于阐明结构-动力学关系。
