Analysis of the Quasi-Cliques of the Stock Markets Graphs

<p>The theme of this work is &quot;Analysis of the Quasi-Cliques of the Stock Markets Graphs.&quot; This topic is relevant, since the study of economic graphs and a new fundamental understanding of their basic properties and their dynamics is very important in modern science. The practical significance of the theme is that the network structures, built on the basis of the stock markets, allow to track patterns of the market, in particular, the relationship between changes in the prices of various stocks.</p><p>One of the most popular models of the stock market is the Market Graph, which is one of the objects of study in this paper.</p><p>The main purpose of this work is to find new ways to identify the link between the changes in share prices on the stock markets.</p><p>On the basis of research objectives the following problems are formulated and solved:</p><p>1. Implement the algorithm of the clique search in sparse graphs with large number of vertices;</p><p>2. Upgrade algorithm for finding quasi-cliques;</p><p>3. Test algorithms and make sure that they work properly;</p><p>4. Choose real data and apply the developed algorithms to them;</p><p>5. Draw conclusions on the basis of the results obtained.</p><p>This work involves the construction of mathematical models of stock markets, the study of their characteristics and properties, and applied analysis of their usefulness. The main achievement of this work is to study the transition from graph cliques to quasi-cliques, which allows a broader look at the relationship between the prices of shares on the market. This transition is a logical generalization of the development of scientists from the beginning of two-thousand years, and gives the opportunity to trace the connection between those actions, between which it would be impossible with the ordinary cliques. This is possible because the quasi-cliques are sufficiently dense, but at the same time are not as rare as regular cliques.</p>