We provide a method to deduce the preferences governing the restructuring dynamics of a network from the observed rewiring of the edges. Our approach is applicable for systems in which the preferences can be formulated in terms of a single-vertex energy function with f(k) being the contribution of a node of degree k to the total energy, and the dynamics obeys the detailed balance. The method is first tested by Monte Carlo simulations of restructuring graphs with known energies; then it is used to study variations of real network systems ranging from the coauthorship network of scientific publications to the asset graphs of the New York Stock Exchange. The empirical energies obtained from the restructuring can be described by a universal function f(k) ~ −k ln k, which is consistent with and justifies the validity of the preferential attachment rule proposed for growing networks.


Originally published in Physical Review E 70(4), 2004. doi:10.1103/PhysRevE.70.046115


network restructuring, linking preferences

Subject Categories

Reverse engineering, Monte Carlo method




The American Physical Society

Publication Date


Rights Holder

©2004 The American Physical Society

Click button above to open, or right-click to save.

Included in

Physics Commons