复杂网络的几何同余与有效贪婪导航性
Geometrical congruence and efficient greedy navigability of complex networks
摘要：
双曲网络被认为是全等的，其潜在的几何和以下测地线在双曲空间被认为是等价于通过拓扑最短路径（TSP）导航。这种几何同余的假设被认为是双曲网络近乎最大效率的贪婪导航的原因。在这里，我们提出了一个复杂的网络措施，称为几何同余（GC），我们表明，可能存在不同的TSP，其投影（pTSP）在双曲空间很大程度上发散，并显着不同，从各自的测地线。我们发现，与目前的信念相反，双曲网络并没有表现出一般的几何一致性和有效的导航性，在nPSO模型生成的网络中，似乎只出现幂律指数接近2。我们的结论是，GC测量也可以影响真实的网络分析，事实上，它显著改变了按性别或年龄分组的结构性大脑连接体。
英文摘要：
Hyperbolic networks are supposed to be congruent with their underlying latent geometry and following geodesics in the hyperbolic space is believed equivalent to navigate through topological shortest paths (TSP). This assumption of geometrical congruence is considered the reason for nearly maximally efficient greedy navigation of hyperbolic networks. Here, we propose a complex network measure termed geometrical congruence (GC) and we show that there might exist different TSP, whose projections (pTSP) in the hyperbolic space largely diverge, and significantly differ from the respective geodesics. We discover that, contrary to current belief, hyperbolic networks do not demonstrate in general geometrical congruence and efficient navigability which, in networks generated with nPSO model, seem to emerge only for power-law exponent close to 2. We conclude by showing that GC measure can impact also real networks analysis, indeed it significantly changes in structural brain connectomes grouped by gender or age.
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