Today we celebrate a recent PNAS paper: “On the origins of hierarchy in complex networks” after years of hard work and rigorous analysis of network hierarchy. The work is led by group member Carlos Rodríguez-Caso and coauthored by Bernat Corominas-Murtra, Joaquín Goñi, and Ricard Solé, all of them attached somehow to our lab; and it debates and defines concepts on network hierarchy, so ubiquitous and perhaps necessary in complex system.
On words by the authors:
In this paper we have studied the hierarchical space of complex networks by defining three axes that allow characterizing the degree and type of hierarchy. The study considers a large variety of webs: technological, ecological, cellular, linguistic and cognitive, among others. We found that most hierarchical organization seems to be a byproduct of random growth: without using selection nor design, just random webs, the observed hierarchical structure can be explained in terms of order “for free”. Large voids in the hierarchical morphospace are also found, and their nature is analyzed using an evolutionary search algorithm.
Although we intuitively appreciate how quickly hierarchy enters a network, the enterprise to formalize the concept turned out to be a mathematical tour de force which we invite you to read now.
Incidentally, Dr. Rodriguez-Caso will be presenting this work at the European Conference in Complex System in Barcelona next week! If you are attending the conference, we gladly invite you over. Very soon we will be posting the activity of lab members in that conference.