K_core of a vertex

I would appreciate knowing about a function which would compute the maximum kcore_ness of a vertex. That is it exists in a k-core graph but not in (k+1)-core graph.

Thank you.

You are looking for the function shell_index.

Thank you so much. I hadn’t realized it before from the documentation. Appreciate it.

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One more quick comment- Unlike degree which is additive (i,e, degree_ALL=degree_IN + degree_OUT), this is not true for coreness- i.e., shell_index_IN + shell_index_OUT seems to be <= shell_index_ALL. I am not sure about why so. Any elucidation will be helpful. Thanks again in advance.

Does a small example help?

When treating this graph as undirected, it is actually the complete graph on three vertices (K_3). The shell index is 2 for all vertices.

However, when treating it as directed, no matter which subgraph you take, there will be a vertex with 0 out-degree (or in-degree). Therefore, the directed coreness is 0, for both the in- and out-cases.

Really a nice counter example. It clarifies. Thx a lot. I appreciate it. Sid