Attributed Networks Formation Models with Application in Social Network Analysis Oksana Pichugina National Aerospace University "Kharkiv Aviation Institute", Chkalova Street 17, Kharkiv, 61070, Ukraine Abstract In the paper, networks characterized by vertices with a number of attributes (attributed networks) are studied. The networks cover a wide class of real-world ones, particularly social networks, making them especially attractive for further development. We analyze how the attributed networks are formed and present several mathematical models built based on their specifics and utilizing well-known classes of graphs – full ones, Erdös-Rényi and Barabasi- Albert random graphs. The computational experiment part includes simulation of test networks for all presented formation models, evaluating their metrics, and confirming their social networks properties. Barabasi-Albert graphs' based model best demonstrated these features. The results can be further used in Community Detection, Cluster Analysis, missing network attribute's restoration and other related Network Analysis problems. Keywords 1 social networks, attributed networks, graph partition, graph cover, aggregation, Erdös- Rényi Random Graphs, Barabasi-Albert Model, complete graph. 1. Introduction Network Analysis (NA) is a research field developed intensively in recent years. Researches in NA study different networks, particularly their social and structural characteristics, investigate statistic and dynamic behaviour of networks, design their formation models, single out their specific features, and solve many other related problems. Among all networks, social ones (SNs) that explore and reflect people and relationships between them are an absolute priority. Why studying and deep understanding SNs is so important? First of all, it provides an understanding of how the world around us is organized. In turn, this allows us to realize what place we occupy in this global human network and how this understanding and knowledge can be used to achieve our goals. At the moment, many features of social networks have been derived. For example, it is known that in the networks there is a so-called "small-world" effect is observable. It manifests itself in a few handshakes between any two people on Earth. At the same time, despite the sparsity of SNs, dense subgraphs called communities are always present in the networks. Many researchers tried to design an ideal model of a social network. However, their attempts have not been crowned with success so far, although they managed to reproduce every single feature of SNs. This paper is dedicated to modelling social networks and other ones in which vertices and edges are decorated with some discrete-valued attributes (attributed networks, ATNs). We propose three mathematical models for such networks based on the combination of isolated random graphs associated with different attributes and their values. Then we confirm experimentally that such networks are closer to SNs than the ones known so far. COLINS-2021: 5th International Conference on Computational Linguistics and Intelligent Systems, April 22 –23, 2021, Kharkiv, Ukraine EMAIL: oksanapichugina1@gmail.com (O. Pichugina) ORCID: 0000-0002-7099-8967 (O. Pichugina) ©฀ 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org)