I see that there is much literature that uses the correlation notion in the equity returns to construct a graph or look into how they are related to one another. If we want to extend this to Credit default swap (CDS) spreads, how can we interpret this correlation? What does this mean in this context? and why is it important to look into the correlation between different CDS returns?
In credit world, there are (at least) two kinds of correlations:
among credit spreads (CDS spreads, Z-spreads, etc)
among defaults (and other credit events).
I suggest you get hold of Youssef Elouerkhaoui's book Credit Correlation: Theory and Practice (2017).