To find the importance of a person, it is common to look at the social network that they are in. Centrality methods consider the importance of a person as a function of their location in the network. For example, in closeness centrality, the importance is defined as a function of how quickly the person can disseminate information to the rest of the network. The shorter the distance of the person to others, the faster they can spread information. Betweenness centrality on the other hand considers the criticality of the person in the whole network. However, it is possible to consider both types of centrality measures at three different levels of analysis.

The first level is the global centrality defined as a function of the whole network. This is the classical centrality measure. We add to this two new measures. We look at local centrality as the centrality of a person within a specific community using only the edges in that community. This measure considers how central a person is within their own community alone. We also look at  community centrality which considers the centrality of the community the person is location in with respect to the network of communities. We show how to compute distance between communities to compute this. It is well-known that social networks contain many communities and many different algorithms have been introduced to this effect. Any of these algorithms can be used to compute these measures.

Given these three measures, we ask: which type of centrality plays a role in determining one’s prominence in a network? The answer is: it depends on the prominence measure. First of all, we can see that in networks with strong community structure, a central community generally represents the mainstream topics for that community. For example, in academic publishing, the papers published in the central community belong to foundational research topics. Peripheral communities on the other hand are more applied topics. The word clouds below show central communities in the DBLP dataset for academic publishing in Computer Science.