An expert finding system allows a user to type a simple text query and retrieve names and contact information of individuals that possess the expertise expressed in the query. This paper proposes a novel approach to expert finding in large enterprises or intranets by modeling candidate experts (persons), web documents and various relations among them with so-called expertise graphs. As distinct from the stateof-the-art approaches estimating personal expertise through one-step propagation of relevance probability from documents to the related candidates, our methods are based on the principle of multi-step relevance propagation in topicspecific expertise graphs. We model the process of expert finding by probabilistic random walks of three kinds: finite, infinite and absorbing. Experiments on TREC Enterprise Track data originating from two large organizations show that our methods using multi-step relevance propagation improve over the baseline one-step propagation based method in almos...