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Composite Centrality


Definition

The composite centrality is a measure for general weighted and directed complex networks, based on measure standardisation and invariant statistical inheritance schemes. Different schemes generate different intermediate abstract measures providing additional information, while the composite centrality measure tends to the standard normal distribution. This offers a unified scale to measure node and edge centralities for complex evolving networks under a uniform framework.
By only using standardised measures (SM), it is straightforward to construct arbitrary composite measures. Having two node measures, A and B, for which ¯A and ¯B denote the corresponding SM, the composite centrality measure is defined by the statistically normalised measure of the sum of the two measures via value-byvalue addition. One has:
Composite Centrality
where σs(·) stands for the sample standard deviation. Ccomp is a new SM carrying an abstract physical meaning depending on the original measures. From here on, standardised measures are denoted with a bar. Having a set of n measures, M ∋ Mi, i ∈ {1, . . . , n}, a generalisation of above takes the form
Composite Centrality

Software

References

  • JOSEPH, A. C. & CHEN, G. 2014. Composite centrality: A natural scale for complex evolving networks. Physica D: Nonlinear Phenomena, 267, 58-67.


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