In this paper, we describe an iterative scheme which is able to estimate the Fiedler value of a network when the topology is initially unknown. The only available information is the one obtained through a random walk process over the network. Our algorithm is based on the Rayleigh quotient optimization problem and the theory of stochastic approximation. We explain the different tools used to construct our algorithm and we describe our iterative scheme. Finally, we illustrate its performance through a numerical study. Index Terms Fiedler value, stochastic approximation, random walk based observations.