Scale-variant topological information for characterizing the structure of complex networks

Understand

The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network.

• We aim to address these problems by introducing a general framework using a method based on topological data analysis.
• By considering the diffusion process at a single specified timescale in a network, we map the network nodes to a finite set of points that contains the topological information of the network at a single scale.
• Subsequently, we study the shape of these point sets over variable timescales that provide scale-variant topological information, to understand the varying topological scales and the complex interactions in the network.