Measuring centrality by a generalization of degree

TL;DR

This paper introduces a generalized degree centrality measure that accounts for the global network structure, improving upon traditional degree centrality by better reflecting node importance and maintaining desirable properties.

Contribution

It proposes a new parametric family of centrality measures called generalized degree, which incorporates global network information to enhance node importance ranking.

Findings

Generalized degree improves node importance differentiation.

The measure is computationally feasible via iterative calculation.

It maintains key properties like rank monotonicity under certain conditions.

Abstract

Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have been developed. This paper proposes a new parametric family of centrality measures called generalized degree. It is based on the idea that a relationship to a more interconnected node contributes to centrality in a greater extent than a connection to a less central one. Generalized degree improves on degree by redistributing its sum over the network with the consideration of the global structure. Application of the measure is supported by a set of basic properties. A sufficient condition is given for generalized degree to be rank monotonic, excluding counter-intuitive changes in the centrality ranking after certain modifications of the network. The measure has a graph interpretation and can be calculated iteratively. Generalized degree is recommended to apply besides degree since it preserves most favourable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish among their importance.