TITLE:
Centrality Measures Based on Matrix Functions
AUTHORS:
Lembris Laanyuni Njotto
KEYWORDS:
Graph, Centrality Measures, Matrix Functions, Kendall Correlation Coefficient, Random Graph Models
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.8 No.4,
September
26,
2018
ABSTRACT: Network is considered naturally as a wide range of
different contexts, such as biological systems, social relationships as well as
various technological scenarios. Investigation of the dynamic phenomena taking
place in the network, determination of the structure of the network and
community and description of the interactions between various elements of the
network are the key issues in network analysis. One of the huge network structure
challenges is the identification of the node(s) with an outstanding structural
position within the network. The popular method for doing this is to calculate
a measure of centrality. We examine node centrality measures such as degree,
closeness, eigenvector, Katz and subgraph centrality for undirected networks.
We show how the Katz centrality can be turned into degree and eigenvector
centrality by considering limiting cases. Some existing centrality measures are
linked to matrix functions. We extend this idea and examine the centrality
measures based on general matrix functions and in particular, the logarithmic,
cosine, sine, and hyperbolic functions. We also explore the concept of
generalised Katz centrality. Various experiments are conducted for different
networks generated by using random graph models. The results show that the
logarithmic function in particular has potential as a centrality measure.
Similar results were obtained for real-world networks.