# Balanced inequality ratio

These are the values of the balanced inequality ratio (P) for all networks to which the statistic applies and for which it was computed. In total, it has been computed for 1,322 networks.

The balanced inequality ratio (P) is the number between zero and one such as the ratio P of nodes with highest degree account for 1 − P of all half-edges. In this definition, each edge is considered to consist of two half-edges, each owned by one node, thus, the degree of a node is the number of half-edges owned by a node, and we can consider statements such as "5% of nodes own 95% of half-edges." The smaller the value, the more inequality is present in the degree distribution. The highest value of one corresponds to the case in the which all nodes have the same degree, i.e., a regular graph. For bipartite networks, we also show the corresponding statistic restricted to left and right nodes (P1, P2). For directed networks, we also show the corresponding statistic restricted to the outdegree and indegree (P+, P).

The full definition of the balanced inequality ratio as well as its properties and relationships to other graph statistics can be found in the KONECT handbook.

References for this statistic:

 [1] Jérôme Kunegis and Julia Preusse. Fairness on the web: Alternatives to the power law. In Proc. Web Sci. Conf., pages 175–184, 2012. [ http ]