A Novel Model for the Calculation of Social Capital in Digital Social Networks

Social capital defined at its simplest is the value that can be ascribed to the social ties between individuals in a social network, an intuitive concept that manifests in something as simple as a friend being able to recommend a good plumber. However despite its simplicity it has been shown to have wide ranging impact throughout a tremendous number of areas from sociology, to business studies, to political science. Prior to recent work social capital analysis has remained the domain of more traditional sociological studies of smaller populations, however with the advent of large scale computational social network analysis there is the opportunity to leverage its techniques to take social capital analysis to new domains and population sizes not previously possible in reasonable time scales.

That accordingly is the purpose of this project, the development of novel social capital analysis techniques capable of working at scale, however also adjusting for the limitations that such a scale brings. Almost uniformly large social networks do not contain the pieces of specific information on their contained nodes which would be more readily captured through a small scale survey. The importance of this information is in differentiating between the forms of social capital, most notable of these being bonding capital resulting from connections between similar people and bridging capital resulting from connections with those who are diverse. Where we lack the information to measure the similarity between individuals we must then attempt to approximate this indirectly. One avenue we have investigated has been the use of community membership as a common property between nodes in a social network. The intuition being that individuals will cluster together in a social network on the basis of some combination of shared attributes and indeed that community membership can be considered an attribute of the structure of the graph itself.

Furthermore a computational approach to social network analysis allows us to make use of machine learning to both approximate measures that are too computationally expensive to calculate in graphs of millions of edges yet are potentially valuable for social network analysis such as decay centrality. It is also possible for us to make use of machine learning to further scrutinise the structures in social networks from which social capital results, a subject which has seen much dispute. We seek to examine the effectiveness of combining various predetermined social network measures which might be associated with social capital as well as attempting to use automated feature extraction in order to escape any assumptions made about the structures. There has been a recent number of works focusing on graph feature extraction primarily either basing their approach on fitting a numeric matrix to random walk samples of the network or using a graph neural network in which the network itself is treated as a neural network and over a series of iterations each node aggregates messages from its neighbours, eventually producing a feature representation for each node. The challenge in adapting such approaches to social capital is that it may not be sufficient to embed structure alone, but rather structure and the resources that an individual can access within that structure. Resources, whether they're information such as the quality of the local plumbers or a loan a friend might give you, can be viewed as the hidden underpinning of social capital and what the structures actually give you access to so it is natural that we should want to capture them as part of our model.