Abstract
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their ability to generate networks with large structural variability. In particular, we consider the statistical constraints which the respective construction scheme imposes on the generated networks. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This makes it possible to infer global features from local ones using regression models trained on networks with high generalization power. Our results confirm and extend previous findings regarding the synchronization properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks in good approximation. Finally, we demonstrate on three different data sets (C. elegans neuronal network, R. prowazekii metabolic network, and a network of synonyms extracted from Roget’s Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models.
Highlights
The development of models for the topology underlying complex interactions in natural systems has attracted much attention in recent research [1,2,3]
Our third main result concerns one specific relation that was detected with our new method: we demonstrate that the synchronization index, a quantity introduced to assess the inertia to synchronization of complex networks [17], depends very strongly on the variance of the in-degree, a fact that may be of special interest for scientists studying network synchronization [10]
Variability of Networks Generated by Different Models Feature variability and dependencies between features vary significantly between different network models
Summary
The development of models for the topology underlying complex interactions in natural systems has attracted much attention in recent research [1,2,3]. We take advantage of two recently developed advanced network models, multifractal networks [13,14] and equilibrium random networks [15] These new classes encompass networks of greater structural diversity in the statistical ensemble than for example Erdos-Renyi graphs or small-world networks and might be more suitable to assess the influence different network properties have on each other. As a first main result, we conclude that multifractal networks and equilibrium random networks are the most variable ones with respect to the generated feature entropy They present a good sampling basis, as only weak correlations between different graph properties are imposed by their construction principle. Our third main result concerns one specific relation that was detected with our new method: we demonstrate that the synchronization index, a quantity introduced to assess the inertia to synchronization of complex networks [17], depends very strongly on the variance of the in-degree, a fact that may be of special interest for scientists studying network synchronization [10]
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