51 Homework VI: Centrality
51.1 Degree Centrality in Undirected Graphs
Rank all the nodes in the graph shown in Figure 51.1 by their degree centrality.
| Node | Degree |
|---|---|
Rank all the nodes in the graph shown in Figure 51.2 by their outdegree centrality and indegree centrality.
| Node | Outdegree | Node | Indegree |
|---|---|---|---|
51.2 Closeness Centrality in Directed Graphs
- In the matrix below, write down the cell entries geodesic distance matrix corresponding to the graph shown in Figure 51.2:
| A | B | C | D | E | F | G | H | I | J | K | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| A | ---- | ||||||||||
| B | ---- | ||||||||||
| C | ---- | ||||||||||
| D | ---- | ||||||||||
| E | ---- | ||||||||||
| F | ---- | ||||||||||
| G | ---- | ||||||||||
| H | ---- | ||||||||||
| I | ---- | ||||||||||
| J | ---- | ||||||||||
| K | ---- |
Using the information in the above matrix, rank all the nodes in the graph shown in Figure 51.2 by their closeness centrality.
| Node | Closeness |
|---|---|
51.3 Relative Betweenness Centrality
Go back to Figure 51.1.
What is the relative betweenness centrality of node C with respect to nodes A and I? (show your work)
51.4 Degree Centralization
Compute the degree centralization of the graph shown in Figure 51.1.