A general conceptual framework for characterizing the ego in a network

•One particular node in a network, referred to as the ego is considered.•A conceptual framework for characterizing the ego is developed.•Using Zipf lists different h-type indices for networks are unified.•This approach is based on mathematical and logical concepts.•This leads to a general framework with large applicability. In this contribution we consider one particular node in a network, referred to as the ego. We combine Zipf lists and ego measures to put forward a conceptual framework for characterizing this particular node. In this framework we unify different forms of h-indices, in particular the h-degree, introduced in the literature. Similarly, different forms of the g-index, the a-index and the R-index are unified. We focus on the pure mathematical and logical concepts, referring to the existing literature for practical examples.