Most of the people would agree on the following definition of Evolution: “any change across successive generations in the heritable characteristics of biological populations”
However those “changes” occur in complex networks (e.g. metabolic, regulatory, ect ect), thus we shall study evolution as the evolution of the correspondent networks.
In his work Anirban Banerjee develops a method to quantify the topological distance to measure and retrace the evolutionary relation and distance between two evolving systems (i.e. population/organism) using normalized graph Laplacian.
This method may allow to measure the evolutionary mechanism that causes functional changes that forces complex systems to adopt new configurations of interaction pattern between their components.
Anirban Banerjee, Structural distance and evolutionary relationship of networks. Biosystems, Volume 107, Issue 3, March 2012, Pages 186–196