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.
There is no agreed definition of social capital in the literature. However, one interpretation is that it refers to those resources embedded in an individual's social network offering benefits to that individual in relation to achieving goals and facilitating actions. This can be viewed as a resource-based interpretation of social capital aimed at the level of individuals. In this paper, we propose a family of social capital measures in line with this interpretation. Our measures are designed for a model of social networks based on weighted and attributed graphs, and cover four dimensions of social capital: (i) access to resources, (ii) access to superiors, (iii) homogeneity of ties, and (iv) heterogeneity of ties. We demonstrate the real-world application of our measures by exploring an illustrative use case in the form of a workplace social network. Index Terms-social capital, measures, social network analysis This work has received funding from the European Union's Horizon 2020 research and innovation programme through the DEVELOP project (under grant agreement no. 688127) and the SoBigData project (under grant agreement no. 654024).
The team formation problem has existed for many years in various guises. One important problem in the team formation problem is to produce small teams that have a required set of skills. We propose a framework that incorporates machine learning to predict unobserved links between collaborators, alongside improved Steiner tree problems to form small teams to cover given tasks. Our framework not only considers size of the team but also how likely are team members going to collaborate with each other. The results show that this model consistently returns smaller collaborative teams.
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