Irregular graphs were initially characterized by Yousef Alavi, Gary Chartrand, Fan Chung, Paul Erdős, Ronald Graham, and Ortrud Oellermann.
[1] They were motivated to define the ‘opposite’ of a regular graph, a concept which has been thoroughly studied and well understood.
[2] Graph theorists thus turned to the issue of local regularity.
The characterization of highly irregular graphs has also been applied to the question of heterogeneity, yet all of these fail to shed enough light on real-world situations.
Efforts continue to be made to find appropriate ways to quantify network heterogeneity.