Average Controllability of Complex Networks With Exponential Degree Distribution

This paper investigates the average controllability of Laplacian dynamical networks characterized by an exponential degree distribution. We introduce a novel configuration network model with an exponential degree distribution, incorporating a degree distribution parameter to adjust the heterogeneity of the distribution. We thoroughly examine the impact of degree distribution and degree correlation on average controllability. Our results reveal that increased heterogeneity in degree distribution tends to enhance average controllability, particularly when edges connect nodes with higher degrees. Moreover, networks with high assortativity exhibit improved average controllability. Building on these findings, we propose two effective strategies for optimizing average controllability. These strategies offer valuable guidance for the design of optimal complex networks in practical settings.