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## Re: [igraph] Coreness Out/In meanings

 From: Tamás Nepusz Subject: Re: [igraph] Coreness Out/In meanings Date: Thu, 16 Jun 2011 20:01:16 +0200

Hi Robin,

Start here:

http://en.wikipedia.org/wiki/Degeneracy_(graph_theory)#k-Cores

Basically, in undirected graphs, the 0-core of the graph is the entire graph. The 1-core is obtained by deleting all the vertices with degree less than 1. The 2-core is obtained by deleting all the vertices with degree less than 2. (Note that things get tricky here because a vertex V may have degree 2 but if it becomes degree 1 after deleting all the original degree 1 vertices from the graph, then V has to be removed as well, until the degree of all the vertices in the remaining graph is at least 2). The 3-core is obtained by removing all the vertices with degree less than 3... and so on. Basically, the k-core is the largest subgraph of the graph within which each vertex has degree at least k. Think of the k-cores like peeling layers off an onion.

Now, with directed graphs, you have k-cores, k-in-cores and k-out-cores. The k-cores are calculated by using the total degrees of the nodes (i.e. sum of indegree and outdegree), the k-in-cores are calculated by using the in-degrees, and the k-out-cores are calculated by using the out-degrees. For instance, the 3-out-core of a graph is the largest subgraph of the graph within which each vertex has an out-degree of at least 3. The "coreness" is basically the index of the highest k-core that a vertex is a member of.

--
T.

On Thursday, 16 June 2011 at 19:17, Robin Shields wrote:

Hello,

Just started using igraph a few days ago and really like it. I'm working with directed, valued data (migration between countries), and analysing coreness. When I use mode="all" there is very little change at all,but I notice very different trends using the coreness mode="out" and mode="in" values - could anyone give a common-sense/lay person's interpretation of what these measurements mean? Or possibly a good/link reference to follow up with? Thanks very much.

Best,
Robin
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