FROM A HARMONIOUS UNIFYING HYBRID PREFERENTIAL MODEL TOWARD A LARGE UNIFYING HYBRID NETWORK MODEL

Abstract

The motivation of this work raises four challenging questions: (1) Why is it that so many generalized random network models exist but they cannot be completely consistent with real-world networks? (2) Are these complex networks fundamentally attached in a random preferential manner without any deterministic attachment for both un-weighted and weighted networks? To answer the first two questions, we propose a harmonious unifying hybrid preferential model (HUHPM) controlled by a total hybrid ratio. (3) Why are social networks mostly positive degree-degree correlation but biological and technological networks tend to possess negative degree-degree correlation? (4) Are there coherent physical ideas and a unification formation mechanism for studies of complex networks? To seek a better answer of all these questions, especially the last two above, we extend the HUHPM to a large unifying hybrid network model (LUHNM), based on introducing two new hybrid ratios. We study the two models above, both numerically and analytically. All findings of topological properties in the network models above can give a certain universally meaningful result, which reveals some nontrivial topological properties, new phenomena, and give a relatively satisfactory answer.