unequal power relationship
An unequal power relationship is a relationship in which some have the power to control others' actions and in which such power is not evenly distributed among all involved. When unequal power relationships become widespread, power networks may form.
UPRs that do not lead to power networks
However, not all unequal power relationships will result in the formation of a power network. A relationship that is entirely voluntary and preserves the right to secede (e.g. a healthy BDSM relationship) will not likely form a long term unequal power relationship.
isolated and/or secret
If the unequal power relation is sporadic and not widespread and reinforced by some social conditioning, no persistent power network can be formed either. An isolated coercive unequal power relationship (e.g. a capitalist secretly kidnapping and enslaving a worker) will not form a power network, since these cannot operate in secret.
The human family is probably the most basic example of an unequal power relationship: human children stand necessarily in an unequal position relative to their human parents. One of those parents may have some profound power over the other reinforced by law, but, this does not necessarily mean that everyone enabled by that power or help from society is going to form a single power network to retain it and extend it. Families are more different in how they handle power than they are similar.
UPRs that lead to PNs
In Marxist discourse the wage slave is the most basic unequal power relationship, and leads directly to the power network called the economic class. Of these the most difficult to organize but most potentially powerful is the proletariat who seek to abolish master-slave relations in the economy.
The command hierarchy of police, paramilitary or military forces necessarily form a power network and must ally with other such to define and control property - that is their sole purpose, according to Marxist discourse, and the protection of "human rights" is merely a cover concern.
guardianship of a commons
The commitment to protect something or someone creates an unequal power relationship between the person who makes the commitment and all those not committed, who might exploit or harm or destroy what is protected. Those can choose to take or harm or attack what is protected, while the guardian can't leave - they are forced by their own commitment to stay and suffer the difficulties.
It is this defensive relationship and common trauma that can turn social networks into a common power network like a non-governmental organization, political party or a civil disobedience group or (looser) anarchization of like-minded defenders of a commons.
Essentially, if no power network is formed, the guardians will necessarily fail when their attackers succeed in forming one - to for instance overwhelm the guardians one by one to take what they are protecting.