Biased random walk on a graph

A biased random walk on a graph is a variation of the classic random walk where the probability of moving in certain directions is influenced or biased by specific factors or preferences. In a standard random walk, a walker starts at a node (or vertex) in the graph and, at each step, chooses one of the neighboring nodes uniformly at random to move to. In contrast, in a biased random walk, the transition probabilities to neighboring nodes are not equal but are weighted according to some bias.