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A random walk on a graph moves from a node to one of its neighbors chosen uniformly at random at each step.
A Markov chain models a system that moves between states where the next step depends only on the current state, not the past.
A Markov chain is a random process where the next state depends only on the current state, not the full history.
Spectral graph theory studies graphs by looking at eigenvalues and eigenvectors of matrices like the adjacency matrix A and Laplacians L and L_norm.