论文标题
复杂网络的几何一致性和有效的贪婪导航性
Geometrical congruence and efficient greedy navigability of complex networks
论文作者
论文摘要
双曲线网络被认为与它们的潜在潜在几何形状是一致的，并且在双曲线空间中遵循测量学的遵循相当于在拓扑最短路径（TSP）中导航。这种几何一致性的假设被认为是双曲线网络几乎有效贪婪导航的原因。在这里，我们提出了一种称为几何质量一致性（GC）的复杂网络度量，我们表明可能存在不同的TSP，其双曲线空间中的投影（PTSP）在很大程度上有所不同，并且与各自的大地测量学有显着差异。我们发现，与当前的信念相反，双曲线网络并未证明一般的几何质量和有效的可通道性，在使用NPSO模型生成的网络中，似乎仅出现接近2的幂律指数。我们结论是通过显示GC措施的结论也可以影响实际的网络分析，实际上它在结构性的脑连接组中都会通过性别或年龄进行了显着变化。
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.
