Formal (Mathematical) Definition of N-Clan?

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I tried many times to find a formal definition for the following important concepts in Graph Theory and Network Analysis:

1) N-Clique.
2) N-Clan.
3) K-Plex.
4) K-Core.

Reference

, but unfortunately I could not find a useful results, So does anyone have a ground knowledge or any idea about the formal definitions of these concepts?

Many Thanks,