Degree-preserving distance compression and topological compressibility of complex networks

Accurately modeling real network dynamics is a grand challenge in network science. The network dynamics arise from node interactions, which are shaped by network topology. Real networks tend to exhibit compact or highly optimized topologies. But the key problems arise: how to compress a network to best enhance its compactness, and what the compression limit of the network reflects? We abstract the topological compression of complex networks as a dynamic process of making them more compact and propose the local compression modulus that plays a key role in effective compression evolution of networks. Subsequently, we identify topological compressibility—a general property of complex networks that characterizes the extent to which a network can be compressed—and provide its approximate quantification. We anticipate that our findings and established theory will provide valuable insights into both dynamics and various applications of complex networks.