Definition
A Markov Chain is a graph G in which each edge has an associated non-negative 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 e0, ..., ed - 1 are the edges out of v. If v has no outgoing edge no further step can be taken. Otherwise, the walk follows edge ei with probability proportional to w[ei] for all i, 0 < = i < d. The target node of the chosen edge becomes the new current node.
#include < LEDA/markov _chain.h >
Creation
| markov_chain | M(graph G, edge_array<int> 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). | ||
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) | |
| returns number of visits to node v. | ||
| double | M.rel_freq_of_visit(node v) | |
| returns number of visits divided by the total number of steps. | ||