Version 5.0 The LEDA User Manual

11.24 Markov Chains ( markov chain )
1. Definition
We consider a Markov Chain to be a graph G in which each edge has an associated nonnegative
integer weight w[e]. For every node (with at least one outgoing edge) the total
weight of the outgoing edges must be positive A random walk in a Markov chain starts
at some node s and then performs steps according to the following rule:
Initially, s is the current node. Suppose node v is the current node and that e 0 , . . . , e d−1
are the edges out of v. If v has no outgoing edge no further step can be taken. Otherwise,
the walk follows edge e i with probability proportional to w[e i ] for all i, 0 ≤ i < d. The
target node of the chosen edge becomes the new current node.
#include < LEDA/graph/markov chain.h >
2. Creation
markov chain M(const graph& G, const edge array& w, node s = nil);
creates a Markov chain for the graph G with edge weights w. The
node s is taken as the start vertex (G.first node( ) if s is nil).
3. Operations
void M.step(int T = 1) performs T steps of the Markov chain.
node M.current node( ) returns current vertex.
int M.current outdeg( ) returns the outdegree of the current vertex.
int
M.number of steps( ) returns number of steps performed.
int M.number of visits(node v)
double M.rel freq of visit(node v)
returns number of visits to node v.
returns number of visits divided by the total number
of steps.