Markov centrality (White and Smyth 2003) is the inverse of the mean first passage time of a random walk into a node: $$M(j) = \left(\frac{1}{n} \sum_{i} m_{ij}\right)^{-1},$$ where \(m_{ij}\) is the expected number of steps from \(i\) to the first visit of \(j\) and \(m_{jj} = 0\).
Arguments
- x
Network input accepted by
centrality.- ...
Further arguments to
centrality.
Details
The walk moves from a node to each of its out-neighbors with equal
probability, so edge weights are ignored. A disconnected network, or a
directed network with a node that has no outgoing edge, gives NA
for every node with a cograph_undefined_measure warning. On a
directed network that is not strongly connected, a node that some other
node cannot reach has an infinite mean passage time, and its score is
NA with the same warning. On connected undirected and strongly
connected directed networks the values equal
centiserve::markovcent().
References
White, S., & Smyth, P. (2003). Algorithms for estimating relative importance in networks. In Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 266-275). doi:10.1145/956750.956782 .