Statistics of paths on graphs with two heavy roots

Abstract

The paper considers the behaviour of the number of paths of length $N$ on graphs with two heavy roots. Such vertices can be entropic traps. Numerical analysis is carried out for graphs with different degrees of root vertices. In the symmetric case, a numerical analysis of the number of paths is performed. It is found that localisation is observed with the same ratio of vertex degrees as in the case of a single root. An analysis of the entropy forces of interaction was also carried out for two roots.