Doctoral Dissertation Research: Spatial Models of Large-Scale Interpersonal Networks

由于地理位置的限制，人类意识到他人或与他人建立联系的能力会随着物理距离的增加而迅速下降。事实上，各种问题，如疾病在人类人口中的传播、文化规范的传播、移徙、种族/族裔隔离以及恐慌或革命的敏感性，都与以距离为基础的人类关系结构有关。然而，社交网络形成的这种空间要素几乎没有受到关注。因此，该项目开发了基于物理距离的数学网络模型，使用已公布的跨空间人际关系数据评估相互竞争的网络模型，并提出了网络结构的衡量标准。使用模拟方法，它确定了上述大规模社会过程与跨越社会团体和组织的社会网络之间的联系。因此，数学方法提供了对人类互动的一般结构的洞察，这些结构塑造了各种类型群体中个人更具体的经历和行为。

Given geographical constraints, the ability of humans to be aware of or establish contact with others falls off rapidly with physical distance. Indeed, problems as diverse as the spread of disease within human populations, the diffusion of cultural norms, migration, racial/ethnic segregation, and susceptibility to panic or revolution have all been linked to the distance-based structure of human relations. Yet, this spatial element of social network formation has received little attention. This project therefore develops mathematical network models based on physical distance, evaluates competing network models using published data on interpersonal relations across space, and presents measures of network structures. Using simulation methods, it identifies the linkages between large-scale social processes, such as those described above, and the social networks that span social groups and organizations. The mathematical methods thus provide insights into the general structures of human interaction that shape the more specific experiences and behaviors of individuals in a variety of types of groups.