Simulating the walk would make the two language arms agree only in
distribution. The transition law is linear, so the whole distribution
is pushed forward exactly – same numbers in both arms and no Monte
Carlo error.
Usage
Randwk(G, start = 1L, steps = 1L)
Arguments
- G
Non-negative weight matrix with positive row sums.
- start
Starting node, 1-based here; the Python arm takes it
0-based. Reported indices are 0-based in both arms.
- steps
Number of steps, non-negative.
Value
List with p, estimate, argmax (0-based),
p_start, n.
Details
Formula: P(j | i) = A_ij / k_i; the returned vector is
e_start P^steps.
References
Lovasz, L. (1996). Random walks on graphs: a survey. In
Combinatorics, Paul Erdos is Eighty, Vol. 2, pages 1-46, Janos
Bolyai Mathematical Society, Budapest.
Examples
G <- matrix(c(0, 1, 1, 1, 0, 0, 1, 0, 0), 3) # a star centred on node 1
Randwk(G, start = 1L, steps = 2L)$p
#> [1] 1 0 0
