Analytical and mathematical description of the structure features of knowledge networks in small cities

Understanding the processes of knowledge localization in small towns is limited by statistical capabilities, differentiation of small town models and ineffi ciency of using generally accepted methodology of spatial analysis. The aim of the article is to justify the methodology of such research and to form the structural characteristics of the knowledge localization network in small towns. Our methodology is based on network theory using classical indicators of network analysis, and also new indicators, taking into account intragroup and intergroup relations. A small city with enterprises as the source of knowledge was taken as an example. On the basis of Rospatent and National Electronic Library data, co-authorship and patent citation networks were built for two key knowledge-carrying enterprises of this city. The study of the intra-urban knowledge localization network revealed, that unlike large networks, and also taking into account the spatialization of knowledge localization processes, the distribution of degrees can obey the power, exponential or logarithmic laws and is infl uenced by the strength of cooperation between patent co-authors. The change of vertex degrees occurs cyclically with a decreasing interval. The study of intercity knowledge localization network is carried out, based on the class of international patent classifi cation, which gives a more accurate characterization of the small city in terms of reception, transfer and formation of codifi ed knowledge. As a result, the position of a small city in the intercity network may depend on the number of city subsets, the size of its own subset and the degree distribution of vertices. Both small town enterprises, being in different technological niches, at the all-Russian level participate in the relevant knowledge fl ows on a par with larger cities, but are poorly included in such a network. The proposed methodology can be extended to the broader issue of small towns. Practical results can be the basis for developing solutions to intensify knowledge fl ows among Russian cities.