ITM Probe is based on discrete-time random walks with boundary nodes and damping. As an example, consider the weighted directed network shown, containing 19 nodes and 44 links. Single-directional links are assigned weight 2 and are indicated using arrows while bi-directional edges are assigned weight 1 and are shown as lines. The first five graphs show the time progress of a random walk in the presence of damping and two absorbing boundary nodes (indicated by octagons). At t = 0, 1000 random walkers start at a single point in the network. At t = 1, they have progressed one step from their origin to the nodes adjacent to it, being distributed randomly in proportion to the weights of the edges leading from the origin. Only 900 walkers remain in the network at t = 1 due to damping: the damping factor μ = 0.9 (dissipation 0.1) means that 10% of walkers are dissipated at each step. At t = 60, most of the walks have terminated, either by dissipation, or by reaching one of the two boundary nodes. The number of walkers terminating at each boundary node depends on their starting location. The final graph shows the probability F
for a random walk starting at any transient node in the network (indicated by circular shape) to terminate at the boundary node on the right-hand side (scaled by 1000). Note that the value indicated in the final graph for the starting node at t = 0 (190) is the same as the final number of walks shown at t = 60 as terminating at the right boundary node.