Strategic network formation is a branch of network science that takes an economic perspective to the creation of social networks, considering that actors in a network form links in order to maximise some utility that they attain through their connections to other actors in the network. In particular, Jackson’s Connections model, writes an actor’s utility as a sum over all other actors that can be reached along a path in the network of a benefit value that diminishes with the path length. In this paper, we are interested in the “social capital” that an actor retains due to their position in the network. Social capital can be understood as an ability to bond with actors, as well as an ability to form a bridge that connects otherwise disconnected actors. This bridging benefit has previously been modelled in another “structural hole” network formation game, proposed by Kleinberg. In this paper, we develop an approach that generalises the utility of Kleinberg’s game and combines it with that of the Connections model, to create a utility that models both the bonding and bridging capabilities of an actor with social capital. From this utility and its associated formation game, we derive a new centrality measure, which we dub “structural hole centrality”, to identify actors with high social capital. We analyse this measure by applying it to networks of different types, and assessing its correlation to other centrality metrics, using a benchmark dataset of 299 networks, drawn from different domains. Finally, using one social network from the dataset, we illustrate how an actor’s “structural hole centrality profile” can be used to identify their bridging and bonding value to the network.

中文翻译：

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结构空洞的中心性：通过战略网络的形成评估社会资本

战略网络的形成是网络科学的一个分支，它从经济的角度出发来创建社交网络，考虑到网络中的参与者形成链接，以便最大化他们通过与网络中其他参与者的联系而获得的某些效用。尤其是，杰克逊的联系模型将参与者的效用写为沿网络中某个路径可到达的所有其他参与者的总和，其效益值随路径长度而减小。在本文中，我们对参与者因其在网络中的位置而保留的“社会资本”感兴趣。社会资本可以理解为与行为者建立联系的能力，以及形成连接原本不相关的行为者的桥梁的能力。这种桥接优势先前已在由Kleinberg提出的另一个“结构漏洞”网络形成游戏中进行了建模。在本文中，我们开发了一种方法，该方法可以概括克莱因伯格游戏的效用并将其与Connections模型的功能相结合，从而创建一种可以对演员与社会资本的联系和桥接能力进行建模的实用程序。从该工具及其相关的形成博弈中，我们得出了一种新的集中度度量，我们将其称为“结构漏洞集中度”，以识别具有较高社会资本的参与者。我们通过将其应用于不同类型的网络并使用从不同域中提取的299个网络的基准数据集来评估其与其他中心性度量的相关性，来分析该度量。最后，使用数据集中的一个社交网络，