Network parameters via equilibrium measures in Schrödinger random walks

Abstract

In this work, we explore the concept of equilibrium measures within the framework of Schr¨odinger random walks on networks. Building on previous work, we demonstrate how these equilibrium measures can be leveraged to compute key network parameters such as the Mean First Passage Time (MFPT) and Kemeny’s constant. By expressing these parameters in terms of generalized inverses of the associated M-matrix, we provide new insights and efficient computational tools for network analysis. The results are particularly applicable to both star and path networks, where we offer explicit formulations for these fundamental quantities. Our findings highlight the importance of equilibrium measures as a powerful tool in the study of complex networks.