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A Power network is a type of contact network where its members can tell other people what to do.
It must be large enough to literally scare or force people to go along with its requests, which makes them orders. This typically requires thousands of people in constant touch with each other.
A political party is the most obvious example. It is typically much larger than a social network but is not one, since people can only call on each other for a small number of reasons, and perhaps at specific times. Also not every member of the network has the same role or right to help.
A corporation may also be a power network if it relies on many power relations to maintain itself - for instance, the right to draw oil from the ground or dump waste without being held responsible for it.
When a power network achieves some stable grasp of political power and daily working control of some important infrastructure, it becomes a power structure. In a democracy the visible power networks represented by the parties compete regularly in an election - but much of the power structure, typically the bureaucracy, does not change, and is typically ignored as a power network in itself.
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