Random Walk Decay Centrality

Random walk decay centrality (Was, Rahwan and Skibski 2019) sums, over all starting nodes $u$, the starting weight $b_u$ times the expected discounted first arrival of a random walk from $u$ at node $v$. With $T_v$ the first arrival time and $a$ the decay factor rwd_decay, $$RWD_v = \sum_u b_u \, E_u\left[a^{T_v}; T_v < \infty\right].$$

Usage

centrality_random_walk_decay(x, rwd_decay = 0.5, rwd_node_weights = NULL, ...)

Arguments

x: Network input accepted by centrality.
rwd_decay: Decay factor $a$, a finite number in $[0, 1)$. Default 0.5.
rwd_node_weights: Nonnegative starting weights $b$, one per node. NULL (default) gives every node weight one. A named vector is matched to the node names.
...: Further arguments to centrality. The measure uses weighted (use edge weights, default TRUE) and normalized (divide by the maximum, default FALSE).

Value

A named numeric vector with one score per node, in input node order.

Details

The walk follows outgoing edges with probability proportional to their weights, and an undirected edge is traversed in both directions. A walk that reaches a node without outgoing edges stops. Loops are kept as transitions that stay at the node unless loops = FALSE. The start counts as an arrival at time zero, so an isolated node scores its own starting weight and rwd_decay = 0 returns the starting weights. Edge weights must be finite and nonnegative, and weighted = FALSE ignores edge weights while keeping rwd_node_weights. Invalid rwd_decay or rwd_node_weights, and raw scores that overflow, raise an error. Example 3 of the paper contains inconsistent numerical values, and the implementation follows Definition 1, equation 6.

References

Was, T., Rahwan, T., & Skibski, O. (2019). Random Walk Decay Centrality. Proceedings of the AAAI Conference on Artificial Intelligence, 33(01), 2197-2204. doi:10.1609/aaai.v33i01.33012197 .

Examples

centrality_random_walk_decay(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   2.066592   1.278368   2.797831   2.173405   2.359979   1.628358   1.233824 
#>   Evaluate     Create      Share 
#>   1.645843   2.129525   1.834672