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# Dynamic Markov Chains ( dynamic_markov_chain )

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/graph/markov_chain.h >

Creation

 dynamic_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).

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. int M.set_weight(edge e, int g) changes the weight of edge e to g and returns the old weight of e

Next: GML Parser for Graphs Up: Graphs and Related Data Previous: Markov Chains ( markov_chain   Contents   Index