Table 1. Summary of some properties found in the onion spectrum.

Scale	Signature in the spectrum	Property
micro	more cores than random	assortativity
	fewer cores than random	disassortativity
meso	exponential decay	tree-like structure
	sub-exponential decay	loopy structure
	change in decay	interesting subgraph
macro	cores	core-periphery structure
	layers	node centrality

“Randomness” here refers to rewiring preserving only degree distribution. All other properties can also be mapped to local connection rules using our network reconstruction rules.