Assessing Applicability of Rising Graph Models for Modeling Network of Knowledge Localization

The article shows practical application of rising graphs for building models of knowledge localization net in cities of different scale. Results of modeling based on three types of rising graphs were compared: they are casual, preferred joining and mixed type that uses different combinations of casualty and preference in arc shaping. The author carried out mathematic description of the model for the latter type of rising graph. Methodology of assessing adequacy and efficiency of the model was put forward, which covers not only identifying the form of dependence between real and theoretical models of distribution of degrees, dynamics of node degree and average local clusterization factor but also analysis of the inner structure of net. As a result the author substantiated impossibility to describe the real net of knowledge localization by a uniform model. Models of rising casual graph and of mixed type are considered the most adequate. Dynamics of clusterization factor can be modeled mainly by graph of preferable joining but with condition of disparity of the indicator rate. The obtained conclusions make the objective of developing models for small nets more acute.