Yakubo K, Korošak D
Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 2):066111. doi: 10.1103/PhysRevE.83.066111. Epub 2011 Jun 20.
The impact of an inhomogeneous arrangement of nodes in space on a network organization cannot be neglected in most real-world scale-free networks. Here we propose a model for a geographical network with nodes embedded in a fractal space in which we can tune the network heterogeneity by varying the strength of the spatial embedding. When the nodes in such networks have power-law distributed intrinsic weights, the networks are scale-free with the degree distribution exponent decreasing with increasing fractal dimension if the spatial embedding is strong enough, while the weakly embedded networks are still scale-free but the degree exponent is equal to γ = 2 regardless of the fractal dimension. We show that this phenomenon is related to the transition from a noncompact to compact phase of the network and that this transition accompanies a drastic change of the network efficiency. We test our analytically derived predictions on the real-world example of networks describing the soil porous architecture.
在大多数实际的无标度网络中，节点在空间中的非均匀排列对网络组织的影响不可忽视。在此，我们提出一个地理网络模型，其中节点嵌入分形空间，通过改变空间嵌入强度，我们可以调节网络的异质性。当此类网络中的节点具有幂律分布的固有权重时，如果空间嵌入足够强，网络是无标度的，度分布指数随分形维数增加而减小，而弱嵌入网络仍然是无标度的，但度指数等于γ = 2，与分形维数无关。我们表明，这种现象与网络从非紧致相到紧致相的转变有关，并且这种转变伴随着网络效率的急剧变化。我们以描述土壤多孔结构的网络这一实际例子来检验我们通过分析得出的预测。
