random_walk {igraph}

Random walk on a graph

Description

random_walk() performs a random walk on the graph and returns the vertices that the random walk passed through. random_edge_walk() is the same but returns the edges that that random walk passed through.

Usage

random_walk(
  graph,
  start,
  steps,
  weights = NULL,
  mode = c("out", "in", "all", "total"),
  stuck = c("return", "error")
)

random_edge_walk(
  graph,
  start,
  steps,
  weights = NULL,
  mode = c("out", "in", "all", "total"),
  stuck = c("return", "error")
)

Arguments

graph

The input graph, might be undirected or directed.

start

The start vertex.

steps

The number of steps to make.

weights

The edge weights. Larger edge weights increase the probability that an edge is selected by the random walker. In other words, larger edge weights correspond to stronger connections. The ‘weight’ edge attribute is used if present. Supply ‘NA’ here if you want to ignore the ‘weight’ edge attribute.

mode

How to follow directed edges. "out" steps along the edge direction, "in" is opposite to that. "all" ignores edge directions. This argument is ignored for undirected graphs.

stuck

What to do if the random walk gets stuck. "return" returns the partial walk, "error" raises an error.

Details

Do a random walk. From the given start vertex, take the given number of steps, choosing an edge from the actual vertex uniformly randomly. Edge directions are observed in directed graphs (see the mode argument as well). Multiple and loop edges are also observed.

For igraph < 1.6.0, random_walk() counted steps differently, and returned a sequence of length steps instead of steps + 1. This has changed to improve consistency with the underlying C library.

Value

For random_walk(), a vertex sequence of length steps + 1 containing the vertices along the walk, starting with start. For random_edge_walk(), an edge sequence of length steps containing the edges along the walk.

Examples

## Stationary distribution of a Markov chain
g <- make_ring(10, directed = TRUE) %u%
  make_star(11, center = 11) + edge(11, 1)

ec <- eigen_centrality(g, directed = TRUE)$vector
pg <- page_rank(g, damping = 0.999)$vector
w <- random_walk(g, start = 1, steps = 10000)

## These are similar, but not exactly the same
cor(table(w), ec)

## But these are (almost) the same
cor(table(w), pg)