Growing random networks under constraints

TL;DR

This paper investigates how random networks evolve under a diameter constraint, revealing that such networks tend to be scale-free with specific degree distribution exponents, which may explain the scale-free nature of biological networks.

Contribution

It demonstrates that maintaining a constant diameter during network growth leads to scale-free structures with exponents between 2 and 3, providing a theoretical explanation for observed biological network patterns.

Findings

Networks under diameter constraints are scale-free with exponents 2-3.

Biological metabolic networks exhibit these scale-free properties.

The results suggest a possible universal principle in network evolution.

Abstract

We study the evolution of a random graph under the constraint that the diameter remain constant as the graph grows. We show that if the graph maintains the form of its link distribution it must be scale-free with exponent between 2 and 3. These uniqueness results may help explain the scale-free nature of graphs, of varying sizes, representing the evolved metabolic pathways in 43 organisms.