Degree-dependent network growth: from preferential attachment to explosive percolation.
We present a simple model of network growth and solve it by writing the dynamic equations for its macroscopic characteristics such as the degree distribution and degree correlations. This allows us to study carefully the percolation transition using a generating functions theory. The model considers a network with a fixed number of nodes wherein links are introduced using degree-dependent linking probabilities pk. To illustrate the techniques and support our findings using Monte Carlo simulations, we introduce the exemplary linking rule pk∝k-α, with α between -1 and +∞. This parameter may be used to interpolate between different regimes. For negative α, links are most likely attached to high-degree nodes. On the other hand, in case α>0, nodes with low degrees are connected and the model asymptotically approaches a process undergoing explosive percolation.
Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium and Flemish Institute for Technological Research (VITO), Boeretang 200, B-2400 Mol, Belgium.
Hans
H
Hooyberghs
Koninklijk Metereologisch Instituut (KMI), Ringlaan 3, B-1180 Brussels, Belgium.
Bert
B
Van Schaeybroeck
Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium.
Joseph O
JO
Indekeu