A graph of knoke information shows strong symmetric ties. It also answers questions such as how separate are the sub-graph ? How large are the connected sub-graphs.Are there particular actors that appear to play network roles ?
We now look at ways to find sub-graphs. One approach is the bottom up manner. A clique extends the dyads by adding members that are tied to all the members in a group.The strict definition can be relaxes to include nodes that are not quite so tied as we will see shortly with n-cliques, n-clans and k-plexes. The notion however is to build it outwards to construct the network. The whole network can then be put together by joining cliques and clique like groupings.
Formally, a clique is the maximum number of actors who have all possible ties among themselves. It can be considered to be a maximal complete sub-graph. Cliques can be viewed in conjunction with the Knoke information matrix mentioned earlier. We might be interested in the extent to which these sub-structures overlap and which actors are more central or more isolated than cliques.
We can examine these by evaluating the actor by actor clique co-memberships.Then we can do hierarchical clustering of the overlap matrix which gives us an idea of the closeness of the cliques. Visually we can see the co-membership and the hierarchical clusterings as matrices formed from the actor and cliques and levels and cliques respectively.
Two major approaches to relaxing the definition for cliques are the N-cliques and N-clan approaches.
In N = 2, cliques we say that an actor is a member of a clique if it is connected to every other member of the clique at a distance greater than one, and in this case we choose two. The path distance of two corresponds to the actor being a friend of a friend.
The cliques that we saw before have been made more inclusive by this relaxed definition of group membership.
The N-clique approach tries to find long and string like groupings instead of the tight discrete ones by the original definitions. It is possible for actors to be connected through others who are themselves not part of the cliques.
To overcome this problem, some restriction is imposed additionally on the total span or path distance between any two members. This is the N-clan approach where all ties are forced to occur by means of others members of the n-clique.
If we are not comfortable with the idea of using a friend of the clique member as a member of the clique, we can use the K-plex approach. In this approach we say that a node is a member of a clique of size n if it has direct ties to n-k members of that clique. This tends to find a relatively large number of small groupings. This shifts focus to overlaps and centralization rather than solidarity and reach.
Courtesy: Hanneman notes
We now look at ways to find sub-graphs. One approach is the bottom up manner. A clique extends the dyads by adding members that are tied to all the members in a group.The strict definition can be relaxes to include nodes that are not quite so tied as we will see shortly with n-cliques, n-clans and k-plexes. The notion however is to build it outwards to construct the network. The whole network can then be put together by joining cliques and clique like groupings.
Formally, a clique is the maximum number of actors who have all possible ties among themselves. It can be considered to be a maximal complete sub-graph. Cliques can be viewed in conjunction with the Knoke information matrix mentioned earlier. We might be interested in the extent to which these sub-structures overlap and which actors are more central or more isolated than cliques.
We can examine these by evaluating the actor by actor clique co-memberships.Then we can do hierarchical clustering of the overlap matrix which gives us an idea of the closeness of the cliques. Visually we can see the co-membership and the hierarchical clusterings as matrices formed from the actor and cliques and levels and cliques respectively.
Two major approaches to relaxing the definition for cliques are the N-cliques and N-clan approaches.
In N = 2, cliques we say that an actor is a member of a clique if it is connected to every other member of the clique at a distance greater than one, and in this case we choose two. The path distance of two corresponds to the actor being a friend of a friend.
The cliques that we saw before have been made more inclusive by this relaxed definition of group membership.
The N-clique approach tries to find long and string like groupings instead of the tight discrete ones by the original definitions. It is possible for actors to be connected through others who are themselves not part of the cliques.
To overcome this problem, some restriction is imposed additionally on the total span or path distance between any two members. This is the N-clan approach where all ties are forced to occur by means of others members of the n-clique.
If we are not comfortable with the idea of using a friend of the clique member as a member of the clique, we can use the K-plex approach. In this approach we say that a node is a member of a clique of size n if it has direct ties to n-k members of that clique. This tends to find a relatively large number of small groupings. This shifts focus to overlaps and centralization rather than solidarity and reach.
Courtesy: Hanneman notes
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