In Wegman's network there are 36 cliques, Figure 14 shows all 36 clique sets with the coauthors. For example, in the relations of coauthors, clique number 11 consists of the nodes (Wegman, Solka, Bryant), clique number 9 consists of the coauthors (Wegman, Solka, W. Martinez, Reid), clique number 2 consists of the actors (Wegman, Solka, W. Martinez, Marchette, Priebe). We can also observe that an actor can be a member of one or more clique such as Solka.

Notice that cliques in a graph may overlap. The same node or set of nodes might belong to more than one clique (some cliques contain more than one member in common). Also, there may be nodes that do not belong to any cliques. However, no clique can be entirely contained within another clique, because if it were the smaller clique then it would not be maximal. Figure 15 shows the clique overlap. There is a considerable overlap among the cliques in the coauthor relation, more than one coauthor belongs to one or more cliques.

Cliques are interesting to study because suppose the actors in one network form two nonoverlapping cliques; and that the actors in another network also form two cliques, but that the memberships overlap (some people are members of both cliques). Where the groups overlap, we might expect that conflict between them is less likely than when the groups do not overlap [1], this is the case with Wegman, Solka, W. Martinez and Marchette. Where the groups overlap, mobilization and diffusion may spread rapidly across the entire network; where the groups do not overlap, traits may occur in one group and not diffuse to the other.

Definition: Two actors are structurally equivalent if they have the same type of ties to the same people.

We now discuss the method of partitioning actors into subsets so that actors within each subset are closer to being equivalent than are actors in different subsets. One way to display the results of a series of partitions is to construct a dendrogram indicating the degree of structural equivalence among the positions and identifying their members. Each level of the diagram indicates the division resulting from a split of the previous subset [4]. A dendrogram thus represents a clustering of the actors, those actors who are connected by branches low in the diagram are closer to being perfectly structurally equivalent, whereas subsets of actors who are joined only through paths high up the diagram are less structurally equivalent (or are not equivalent at all). In brief, the lowest position in the diagram indicates that every actor is different while the highest position indicates that all actors are the same; what is in between is more important in terms of structural equivalence. Figure 16 shows the cluster diagram of Wegman's network.

4.5 Blockmodeling

Definition: A blockmodel is the process of identifying positions in the network. A block is a section of the adjacency matrix "a group of people" structurally equivalent. It consists of two things according to Wasserman and Faust [4]:

• A partition of actors in the network into discrete subsets called positions.

• For each pair of positions a statement of the presence or absence of a tie within or between the positions on each of the relations.

A blockmodel is thus a hypothesis about a multirelational network. It presents general features of the network, such as the ties between positions, rather than information about individual actors.

A blockmodel is a simplified representation of multirelational network that captures some of the general features of a network's structure. Specifically, positions in a blockmodel contain actors who are approximately structurally equivalent. Actors in the same position have identical or similar ties to and from all actors in other positions. Thus, the blockmodel is stated at the level of the positions, not individual actors.

Figure 17 shows these two clumps clustered in the upper left corner of the adjacency matrix, there is a total of four clusters in the graph. Each member of these clusters in structurally equivalent. The graph is based on random start blockmodeling applied on the network using structural equivalence while setting the number of cluster to be four.

5 Advanced Analysis

5.1 Discarding Weak Ties

We next present some discussion on the network excluding the edges having weight=1, i.e. all the coauthors who wrote with Wegman only once. The basic concept is that actors who communicated "wrote" with Wegman only one time are most likely to be students who graduated and are no longer connected to Wegman in some sense or coauthors who have weak ties with Wegman at the current time. In conclusion, these are the ones with minimal impact on the network. We will assume that all the coauthors with tie strength being one have not coauthored with Wegman and therefore will be treated as isolated nodes in the network. Figure 18 shows the network without the edges with frequency 1 together with the corresponding edge weight. As before, nodes' color and size are set by the attribute "node degree" while edges' color and thickness are set by the attribute "tie strength".

=

Figure 19 shows the cliques not including the nodes with edge weight=1, the number of cliques is 14.

Figure 20 shows the network without Wegman. Clearly, the network is disconnected with fewer components. There are three subgroups that are still relatively strong, these subgroups