Institute for Applied Computing "Mauro Picone", National Research Council of Italy, Via dei Taurini 19, 00185, Rome, Italy.
"Enrico Fermi" Research Center (CREF), Via Panisperna 89A, 00184, Rome, Italy.
Sci Rep. 2022 Oct 28;12(1):18206. doi: 10.1038/s41598-022-22798-6.
Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose properties may be tuned upon the characteristics of a given population. In the present paper, we introduce the Fitness-Corrected Block Model, an adjustable-density variation of the well-known Degree-Corrected Block Model, and we show that the proposed construction yields a maximum entropy model. When the network is sparse, we derive an analytical expression for the degree distribution of the model that depends on just the constraints and the chosen fitness-distribution. Our model is perfectly suited to define maximum-entropy data-driven spatial social networks, where each block identifies vertices having similar position (e.g., residence) and age, and where the expected block-to-block adjacency matrix can be inferred from the available data. In this case, the sparse-regime approximation coincides with a phenomenological model where the probability of a link binding two individuals is directly proportional to their sociability and to the typical cohesion of their age-groups, whereas it decays as an inverse-power of their geographic distance. We support our analytical findings through simulations of a stylized urban area.
网络模型在解释和再现经验观察到的模式方面起着重要作用。合适的模型可用于在保留网络某些特征的同时对观察到的网络进行随机化，或者生成其属性可根据给定群体特征进行调整的合成图。在本文中，我们引入了适应性密度变化的 Fitnes-Corrected Block Model，这是广为人知的 Degree-Corrected Block Model 的一个可调密度变体，并证明了所提出的构造产生了最大熵模型。当网络稀疏时，我们推导出模型的度分布的解析表达式，该表达式仅取决于约束和所选适应度分布。我们的模型非常适合定义最大熵数据驱动的空间社交网络，其中每个块标识具有相似位置（例如，住所）和年龄的顶点，并且可以从可用数据推断出预期的块到块邻接矩阵。在这种情况下，稀疏状态下的逼近与一种现象模型一致，其中连接两个人的链路的概率与他们的社交能力和他们年龄组的典型内聚力成正比，而与他们的地理距离成反比。我们通过对一个风格化的城市区域的模拟来支持我们的分析结果。
