How do nation states exert power through networks?

Because I am a very visual learner, this question really resonated with me. Well, not so much the question, but the many diagrams that Mr. CHayden wrote on the board. These diagrams help us to understand the nature of networks and how they ‘work’.  My perception of a network was very literal—I assume a network needs to be a net that works; that is, a series of interconnected nodes whose linkages portray the nature of the relationship.  However, understanding the Arsenault article through the use of diagrams helped me to understand the use of dyads and monads. (Monads still do not make that much logical sense to me, because I do not understand the idea that the node does not connect with anything else...)  A amateurish answer of the question stated above, with the basic understanding of what a network is that states exert power through a network hierarchy. One model that Mr. CHayden drew shows just this relationship.

<--This is the basic model. However, in a real-life scale, we run into issues of complexity. This very complexity is where the power is garnered.

State elected officials exert power over their subordinates- bureaucratic officials, who exert power over their subordinates, and their constituents, who then exert power over corporations and businesses that they patronize.