What are the conditions for two graphs to be in correspondence?
I know for isomorphic - Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic.
But how is isomorphic different from correspondence? does correspondence only means that number of vertices should be same?
I was reading this research paper when the author says "We assume that the connectivity relationship is symmetric, so the networks may be represented as symmetric weighted graphs.We also assume that the two graphs vertices are already in correspondence, and thus in this work do not address the graph-matching problem"
Source: David K. Hammond, Yaniv Gur, Chris R. Johnson, 2013 IEEE Global Conference on Signal and Information Processing, "Graph diffusion distance: A difference measure for weighted graphs based on the graph Laplacian exponential kernel" https://www.sci.utah.edu/publications/hammond13/Hammond_GlobalSIP2013.pdf