h-Degree as a basic measure in weighted networks

► 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. We introduce the h-degree of a node as a basic indicator for weighted networks. The h-degree ( d h) of a node is the number d h if this node has at least d h links with other nodes and the strength of each of these links is greater than or equal to d h. 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.