## The effect of context on the importance of actors in networks

*Mirco SchÃ¶nfeld, Juergen Pfeffer*

To assess the importance of actors in networks, centrality measurements are the method of choice. They are easy to obtain and, at the same time, provide a versatile interpretability adaptable to the meaning of nodes and edges. Yet, current centrality measurements utilize structural information alone. In real-world situations, however, actors and connections among them are subject to contextual settings that might have a significant influence on both actors and connections. Such real-world observations are often modeled using attributed networks in which contextual information can be associated as attributes to nodes and edges. But, this information is disregarded when it comes to evaluating importance of actors in terms of network centrality measurements.
If there is attribute information on nodes and edges one might consider the use of multilayer networks, multiplex networks, or the like. Such networks contain multiple types of relations which are represented on distinct layers. The kind of attributed networks we consider in this work, however, are not translatable into multilayer representation. For one thing, this is because we focus on attributed networks which denote a single type of relation only. The only way to identify different types of relations would be to segregate the network based on attribute information. But, for another thing, we focus on attribute data that is multivariate or complex itself. Hence, such contextual information either do not allow for an obvious segregation or it would render a multilayer view rather complicated.
In this talk, we propose a method for obtaining shortest-path based centrality measurements for attributed networks that exploit attribute information of nodes during shortest-path calculations. By evaluating attribute information in shortest-path calculations, we operationalize the notion of individual outreach within certain contexts, i.e. take into account that every node has an individual view on its surroundings which may be subject to individual contextual constraints. We obtain the node-individual view on the network by comparing a node's attribute information with attribute information of all other nodes in the network and weight the corresponding shortest paths accordingly allowing weights of zero which effectively prohibits certain paths. This results in a set of shortest-paths, or geodesics, that is representing the view of a single node only rather than a all geodesics of the whole network. Consequently, this set of geodesics is only valid for obtaining a centrality value for an individual node.
To illustrate the usefulness of this approach, we will evaluate an attributed network of co-authorship of scientific publications in which context is derived from the underlying publications. By considering context information in shortest-path based centrality measurements, we can grasp the importance and impact of individual researchers by evaluating their co-authorship connections, and contrast this picture with data on their specialization and diversification with respect to certain fields of research.← Schedule