Ferretti Luca, Cortelezzi Michele
Centre de Recerca en Agrigenòmica and Departament de Ciència Animal i dels Aliments, Universitat Autònoma de Barcelona, Bellaterra, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jul;84(1 Pt 2):016103. doi: 10.1103/PhysRevE.84.016103. Epub 2011 Jul 8.
We obtain the degree distribution for a class of growing network models on flat and curved spaces. These models evolve by preferential attachment weighted by a function of the distance between nodes. The degree distribution of these models is similar to that of the fitness model of Bianconi and Barabási, with a fitness distribution dependent on the metric and the density of nodes. We show that curvature singularities in these spaces can give rise to asymptotic Bose-Einstein condensation, but transient condensation can be observed also in smooth hyperbolic spaces with strong curvature. We provide numerical results for spaces of constant curvature (sphere, flat, and hyperbolic space) and we discuss the conditions for the breakdown of this approach and the critical points of the transition to distance-dominated attachment. Finally, we discuss the distribution of link lengths.
我们获得了一类在平坦和弯曲空间上增长网络模型的度分布。这些模型通过由节点间距离函数加权的优先连接来演化。这些模型的度分布类似于比安科尼和巴拉巴西的适应度模型，其适应度分布取决于度量和节点密度。我们表明，这些空间中的曲率奇点会导致渐近玻色 - 爱因斯坦凝聚，但在具有强曲率的光滑双曲空间中也能观察到瞬态凝聚。我们给出了常曲率空间（球面、平坦空间和双曲空间）的数值结果，并讨论了这种方法失效的条件以及向距离主导连接转变的临界点。最后，我们讨论了链路长度的分布。
