Identifying stable network structures and sets of key players using a W-covering perspective

In evaluating and benchmarking positions of nodes within networks, several network statistics can be considered. A new benchmark is introduced that can be used to investigate whether or not a node is outperformed by another node regarding the connections to some fixed set W of nodes. Networks where these subdued positions do not exist are called W-stable. In this paper special attention is paid to minimal W-stable (random) networks, where W is the set of nodes having a degree crossing some fixed number. The notion of W-covering also makes possible to disclose an alternative definition and role of key players in social networks.