Algebraic connectivity of multi-agent systems with homogeneous substructure

Abstract

This paper presents a method for finding the algebraic connectivity of multi-agent systems with homogeneous substructure. The systems consist of several homogeneous substructure where only one vertex is connected with main structure. Their algebraic connectivity can be calculated from properties of graphs corresponding to substructure and main structure. Also, it is shown that the algebraic connectivity of an entire system is less than or equals to that of substructure and that of main structure.