h-Degree as a basic measure in weighted networks

We introduce the h-degree of a node as a basic indicator for weighted networks. The h-degree (dh) of a node is the number dh if this node has at least dh links with other nodes and the strength of each of these links is greater than or equal to dh. Based on the notion of h-degree other notions are developed such as h-centrality and h-centralization, leading to a new set of indicators characterizing nodes in a network.

► The h-degree is introduced as a basic measure in weighted networks.
► Based on the notion of an h-degree, h-centrality, h-centralization and related parameters are developed.
► These new indicators add to the toolbox of network studies.