Network similarity
How to measure Similarity (or distance) between networks? What if two networks have different size or density?
In considering Graph isomorphism, we are interested in whether two given networks can be mapped to each other perfectly. Graph matching or Network alignment deals with the problem of aligning two networks as much as possible when these two networks are not necessarily isomorphic. Graph matching is the term mostly used in computer science and Network alignment is used in biological contexts (e.g., aligning two Protein protein interaction networks from two species). Graph kernels are similarity functions used for Kernel method.
There are many ways to think about similarity. We can think about macroscopic properties, such as degree distribution, average path length, etc., or mesoscopic structure^{1}, or microscopic properties. Recently, there have also been embeddingbased approaches.
 https://link.springer.com/chapter/10.1007/9783540698128_51
 Bagrow et al., Portraits of Complex Networks, Bagrow & Bollt, An informationtheoretic, allscales approach to comparing networks
 Koutra et al., DELTACON: A Principled MassiveGraph Similarity Function
 Shimada et al., Graph distance for complex networks
 Identifying network structure similarity using spectral graph theory
 Torres et al., Nonbacktracking cycles: length spectrum theory and graph mining applications
 SimGNN: A Neural Network Approach to Fast Graph Similarity Computation
Brain network

e.g., Onnela2012taxonomies and Gates2019element ↩