The MSS of Complex Networks with Centrality Based Preference and Its Application to Biomolecular Networks

Networks are employed to represent many real world complex systems. For biological systems, biomolecules interact with each other to form so-called biomolecular networks. The explorations on the connections between structural control theory and biological networks have uncovered some interesting biological phenomena. Recently, some studies have paid attentions to the structural controllability of networks in notion of the minimum steering sets (MSSs). However, the MSSs for a complex network are not unique. Therefore, it is meaningful to find out the most special one with some centrality-based preference. The MSS of a network which has the maximum (minimum) average value of a certain centrality among all possible MSSs of the network can be identified by our method. Then we apply the method to the human liver metabolic network and find that centralities of steering nodes in different MSSs can be remarkably different. In addition, we observe that, for some centralities, the liver cancer reactions are significantly enriched in the MSSs with the minimum average centrality value. This result suggests that when investigating the controllability of biomolecular networks, the centralities, which could provide more meaningful biological information, can be taken into consideration.