Victor Kokhov – Associate Professor, Department of Higher Mathematics, Faculty of Economics, National Research University Higher School of Economics.
Address: 20, Myasnitskaya str., Moscow, 101000, Russian Federation.
E-mail: viktorkokhov@rambler.ru

Victor Kokhov – Student of MSc Program, Department of Applied Mathematics, Institute of Automation and Computer Technology, National Research University «Moscow Power Engineering Institute» (NRU MPEI).
Address: 14, Krasnokazarmennaya str., Moscow, 111250, Russian Federation.
E-mail: viktor-kokhov@ya.ru

Normally, graph theory models and methods are used to analyze relationships between complex structure elements of various nature. In such a case, relationships between elements are continuous and will not change with time. Such graphs are called “statistical” graphs. When relationships between structural elements are changing with time, then the traditional “statistical” graphs become inapplicable for generation and modeling. To date, the most important trend is Development of graph analysis methods with changeable structure  in time (temporal orgraphs or Т-orgraphs). 

The purpose of this study is reviewing new methods for T-orgraph structural analysis taking account of importance of the given fragments. The analysis focuses on building up new complexity models allowing to investigate changes to both local (fragments) and global (structure in general) features of T-orgraphs, определять сходство Т-орграфов и выявлять тенденции изменения свойств.

The study suggests a system of six models characterizing global features of Т-orgraphs. All of these models characterize structural spectral complexity of Т-orgraphs in extendable fragment ranges. There are two approaches suggested for structural analysis of T-orgraph local properties: on a continuous structure and Т-orgraph structure divided into parts upon  deleting certain peaks or curves. Comparison of two approaches to calculation of contribution by fragments to overall complexity has resulted into separating the first approach a more accurate.

The suggested complexity models can be viewed as a hierarchical clarifying analysis system allowing to resolve issues on investigation of T-orgraph dynamical properties, particularly monotones of their change. The complexity models allow to analyze the significance of temporal orgraphs and their fragments, and also analyze their change tendencies. An example of application of the suggested models and methods can be performance change monitoring for Т-orgraphs as actor communication models within corporate social networks for managers to take reasoned management decisions. T-orgraph analysis methods have been implemented in Graph-model Workshop System and used in educational process at Higher School of Economy National Research University and Moscow Energy Institute National Research University.