Usher Institute, University of Edinburgh, Edinburgh, UK.
Health Data Research UK, London, UK.
Sci Rep. 2021 Jan 21;11(1):1976. doi: 10.1038/s41598-021-81547-3.
Networks of disparate phenomena-be it the global ecology, human social institutions, within the human brain, or in micro-scale protein interactions-exhibit broadly consistent architectural features. To explain this, we propose a new theory where link probability is modelled by a log-normal node fitness (surface) factor and a latent Euclidean space-embedded node similarity (depth) factor. Building on recurring trends in the literature, the theory asserts that links arise due to individualistic as well as dyadic information and that important dyadic information making up the so-called depth factor is obscured by this essentially non-dyadic information making up the surface factor. Modelling based on this theory considerably outperforms popular power-law fitness and hyperbolic geometry explanations across 110 networks. Importantly, the degree distributions of the model resemble power-laws at small densities and log-normal distributions at larger densities, posing a reconciliatory solution to the long-standing debate on the nature and existence of scale-free networks. Validating this theory, a surface factor inversion approach on an economic world city network and an fMRI connectome results in considerably more geometrically aligned nearest neighbour networks, as is hypothesised to be the case for the depth factor. This establishes new foundations from which to understand, analyse, deconstruct and interpret network phenomena.
不同现象的网络——无论是全球生态系统、人类社会制度、人类大脑内的网络，还是微观尺度的蛋白质相互作用网络——都表现出广泛一致的结构特征。为了解释这种现象，我们提出了一种新理论，其中链接概率由对数正态节点适应性（表面）因素和潜在欧几里得空间嵌入节点相似性（深度）因素共同建模。该理论基于文献中的反复出现的趋势，断言链接的产生既源于个体因素，也源于对偶因素，而构成所谓深度因素的重要对偶信息被构成表面因素的这种本质上非对偶信息所掩盖。基于该理论的建模在 110 个网络中明显优于流行的幂律适应性和双曲几何解释。重要的是，模型的度分布在小密度下类似于幂律分布，在较大密度下类似于对数正态分布，为长期以来关于无标度网络的本质和存在的争论提供了调和解决方案。通过对经济世界城市网络和 fMRI 连接组进行表面因素反转方法验证，得到了更符合几何结构的最近邻网络，这与深度因素的情况假设相符。这为理解、分析、解构和解释网络现象奠定了新的基础。
