K-Clan detection based on a given connected Graph I have the following definition of the K-Clan: A k-clan is a k-clique where the diameter of the corresponding sub-graph is at most k. and here according to the graph bellow I do not know why 135 is not 2-Clan, but they are still 2-Clique,, I am wonderful if it is also 2-Clan since still satisfies the condition/definition of K-Clan !? the same 246 why not 2-Clan ? Any suggestion please.. !enter image description here

135 is not a $2$-clan because the induced subgraph on 135 does not have diameter at most 2 (it is not connected, so the diameter is infinite). 135 forms a 2-clique because it is a set in the graph where the pairwise distances between the points is at most 2. $k$-clique looks at sets inside the whole graph. $k$-clan looks at induced subgraphs.