Communication and Contacts in Massively Interconnected Systems (MIS): Part 3: Theory of Connectivity Functions, Group Characteristics of Connectedness and Rent’s Rule


By Pavel Barseghyan, PhD 

Yerevan, Armenia


Theory of connectivity functions between the elements of large systems can be used for different purposes including analytical derivation of the group connectedness characteristics.

The experience of the development of quantitative sciences suggests that having reliable mathematical models at the level of system’s elements it is possible to build adequate quantitative representations at the level of the groups of elements.

For this purpose people usually use different forms of superposition principle which is a mean for finding corresponding resulting fields of the groups of elements for different types of fields.

The matter here is that similar to the electric charge and gravitational mass, which respectively produce an electric field and a gravitational field, the elements of large MIS create connectivity fields in their vicinity [1].

Like the electric or gravitational field, the connectivity of MIS as a whole can also be described by high-level or group level models using superposition principle for connectivity fields of elements.

From the point of view of adequate quantification of social phenomena and processes, this means that having mathematical models of the individual’s connectivity with the environment in the form of connectivity functions, it is possible to build analytical models to describe connectedness between people at the level of human groups.

This third part of the paper is devoted to the representation of group characteristics of connectedness based on the theory of connectivity functions for simple one-dimensional and homogeneous massively interconnected systems.

Connectivity characteristics of the groups of elements

To study connectivity characteristics of the groups of elements with the aid of connectivity functions let’s consider again their regular location along the x-axis [1, 2].

With this arrangement, each element of the system has its own connectivity function, which is shifted with respect to the previous element by one step (Fig. 1). For example, if the equation of the right branch of connectivity function of the element located at the point 0 is, then the equation of the same branch of the element at point 1 is. Accordingly, the same equation for the element at any arbitrary point will be.

Combination of the basic properties of connectivity functions with their motion along the x-axis allows us to derive analytically all group characteristics of connectivity of an arbitrary number of N elements.


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About the Author 

pavel-barseghyanflag-Armenia-USAPavel Barseghyan, PhD     

Yerevan, Armenia

Plano, Texas, USA

Dr. Pavel Barseghyan is a consultant in the field of quantitative project management, project data mining and organizational science. Has over 40 years’ experience in academia, the electronics industry, the EDA industry and Project Management Research and tools development. During the period of 1999-2010 he was the Vice President of Research for Numetrics Management Systems. Prior to joining Numetrics, Dr. Barseghyan worked as an R&D manager at Infinite Technology Corp. in Texas. He was also a founder and the president of an EDA start-up company, DAN Technologies, Ltd. that focused on high-level chip design planning and RTL structural floor planning technologies. Before joining ITC, Dr. Barseghyan was head of the Electronic Design and CAD department at the State Engineering University of Armenia, focusing on development of the Theory of Massively Interconnected Systems and its applications to electronic design. During the period of 1975-1990, he was also a member of the University Educational Policy Commission for Electronic Design and CAD Direction in the Higher Education Ministry of the former USSR. Earlier in his career he was a senior researcher in Yerevan Research and Development Institute of Mathematical Machines (Armenia). He is an author of nine monographs and textbooks and more than 100 scientific articles in the area of quantitative project management, mathematical theory of human work, electronic design and EDA methodologies, and tools development. More than 10 Ph.D. degrees have been awarded under his supervision. Dr. Barseghyan holds an MS in Electrical Engineering (1967) and Ph.D. (1972) and Doctor of Technical Sciences (1990) in Computer Engineering from Yerevan Polytechnic Institute (Armenia).  Pavel’s publications can be found here: http://www.scribd.com/pbarseghyan and here: http://pavelbarseghyan.wordpress.com/.  Pavel can be contacted at [email protected]