Peter-
Here is what it means:
A k-core is a maximal group of actors, all of whom are connected to some number (k) of other members of the group. To be included in a k-plex, an actor must be tied to all but k other actors in the group. The k-core approach is more relaxed, allowing actors to join the group if they are connected to k members, regardless of how many other members they may not be connected to. By varying the value of k (that is, how many members of the group do you have to be connected to), different pictures can emerge. K-cores can be (and usually are) more inclusive than k-plexes. And, as k becomes smaller, group sizes will increase.
NetDraw includes a tool for identifying and coloring a graph according to its K-cores. The UCINET algorithm for identifying K-cores is located at
Network>Regions>K-Core.
In our example data, if we require that each member of a group have ties to 3 other members (a 3-core), a rather large central group of actors is identified {1,2,3,4,5,7,10}. Each of the seven members of this core has ties to at least three others. If we relax the criterion to require only two ties, actors 8 and 9 are added to the group (and 6 remains an isolate). If we require only one tie (really, the same thing as a component), all actors are connected.
The k-core definition is intuitively appealing for some applications. If an actor has ties to a sufficient number of members of a group, they may feel tied to that group -- even if they don't know many, or even most members. It may be that identity depends on connection, rather than on immersion in a sub-group.
This from:
http://faculty.ucr.edu/~hanneman/nettext/C11_Cliques.html#kcoreIn our large network a k-core with a high value means those people in a kcore of 5 are attached to at least five other people in a cluster whoa re also attached to at least five of the same cluster. Its looser than a clique definition which is very strict and hard to see at cliques of size 4,5,6. There can be different K-cores of 4,5,6 and so on that may or may not be connected.
What this means precisely will be up to you to interpret. In our data, the K core of six is zach evans an is basketball friends. K-cores of 2 may not be that interesting individually as there are many.
Does this help?