Network heterogeneity in an undirected network

Networks may be homogeneous in the sense that all nodes are of the same type or they may be heterogeneous in the sense of containing many types of nodes. Once a choice about the types of nodes to be distinguished is made, it is still an open question how to define an acceptable measure of heterogeneity. A proposal to solve this problem is provided in this contribution. In our view the term heterogeneity in a network implies that links between nodes of different type are gauged positively, while links between nodes of the same type should not contribute to a heterogeneity value. Hence a high heterogeneity value refers to a tightly woven net between dissimilar things. We value this property so high that networks without external links receive the same heterogeneity value as homogeneous networks. Concretely, units that determine the value of a heterogeneity measure are links between nodes of different types. These considerations lead to a new measure for heterogeneity derived from a true diversity measure. We claim that we are now able to measure the heterogeneity of networks in a much more precise way than was possible before. An example related to interdisciplinarity is provided. As heterogeneous networks are ubiquitous in the real world, such as in molecular networks, disease networks and trade networks our approach has universal applicability.