A power network is a group of people who can make something happen despite resistance by others. Because such networks directly compete, the only real defense against them is to create a new one, or ally with another to merge into bigger power networks. A company or political party or non-governmental organization are examples of power networks. They often include or make use of social networks, creative networks and are, like those, based on a huge contact network - extending always to thousands or millions of people, but only using them for specific purposes (like voting).
The Simple English article on 'power network' has more detail.