Regular equivalence in informed network search

Search in networks is defined as a process in which an agent hops from one network node to another by traversing network links in search for given nodes. The simplest example of network search is a random walk where the agent selects a link uniformly at random from all outgoing links of the current node. On contrary, in an informed search the agent possesses (partial) background knowledge of the network. This background knowledge steers the agent´s decisions when selecting the next link to traverse. The background knowledge of the network can be represented as a similarity matrix with similarities between pairs of nodes known to an agent. This matrix can be calculated in various ways in order to model various search scenarios or to best fit needs of an application. For example, similarities based on node degrees or some external information about the nodes have been commonly used in the past. In this paper we evaluate the measures that capture regular equivalence of nodes in a network with respect to their suitability as a similarity metric to inform search in networks. In particular we are interested in the properties of Katz similarity for this task.