Title: Scale-variant Topological Information for Characterizing Complex Networks,
Abstract: Real-world networks are difficult to characterize because of the variation of
topological scales, the non-dyadic complex interactions, and the fluctuations.
Here, we propose a general framework to address these problems via a
methodology grounded on topology data analysis. By observing the diffusion
process in a network at a single specified timescale, we can map the network
nodes to a point cloud, which contains the topological information of the
network at a single scale. We then calculate the point clouds constructed over
variable timescales, which provide scale-variant topological information and
enable a deep understanding of the network structure and functionality.
Experiments on synthetic and real-world data demonstrate the effectiveness of
our framework in identifying network models, classifying real-world networks
and detecting transition points in time-evolving networks. Our work presents a
unified analysis that is potentially applicable to more complicated network
structures such as multilayer and multiplex networks.