The article contains a mathematical model of parametrized network of knowledge exchange. It considers a process of knowledge spreading among a group of people united by common professional interests (a company or its sub-unit). A network is described by a fuzzy graph where vertices stand for individuals and edges – for contacts between them. A fuzzy set of edges defines the process quality characteristics that have direct influence on the result: coincidence of professional interests of individuals (in the model – cognitive potential of knowledge transfer) and evaluation of communication activity between them (how often they communicate – communication intensity). The first parameter is defined on the base of knowledge structure of individuals (for particular knowledge domain). The second one – communication intensity – is counted on information of communication occurrence (one-on-one communication, in groups, round tables and other ways of communication are taken into account). On the base of the quality parameters of relation between members of a group the model define clusters in a network (connected components in the graph theory) – subgroups of individuals that have strong productive communication among them. The model has a set of overall process characteristics of the process of knowledge spreading and may be used for analysis of network states in different timestamps and as consequence of all that – for knowledge management support. Information for analysis can be retrieved for corporate social networks. The model itself and its instruments can be added as an add-on to corporate networks to sustain knowledge management in organization. The article contains an example of the model use (calculation, analysis, illustration of fuzzy graphs). It defines the model’s advantages and probable ways of improvement.