In this paper, the dynamics of the consumer preference change, affected by a word-of-mouth communication (w-o-m), is investigated. Is seems to be interesting, how the network structure parameters (number of contacts, diversity of groups, possibility to change the source of information) influence the consumer behavior on the duopoly market. In the model presented in this article, a two-dimensional cellular automaton (CA) is used which enables to simulate the number of informal contacts, by adoption of variety of different neighborhood radii and also different neighborhood shapes. Although, one type of networks is examined in this article (CA type model), different network structure parameters are obtained by changing the above neighborhood parameters together with varied population densities and an agent movement possibility. The results indicate that the network structure parameters, are of particular importance in the processes of preferences' change.