Homework VI: Centrality

Figure 1: An undirected graph.

Degree Centrality in Undirected Graphs

Rank all the nodes in the graph shown in Figure 1 by their degree centrality.

Node	Degree

Figure 2: A directed graph.

Rank all the nodes in the graph shown in Figure 2 by their outdegree centrality and indegree centrality.

Node	Outdegree	Node	Indegree

Closeness Centrality in Directed Graphs

• In the matrix below, write down the cell entries geodesic distance matrix corresponding to the graph shown in Figure 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 2 by their closeness centrality.

Node	Closeness

Relative Betweenness Centrality

Go back to Figure 1.

What is the relative betweenness centrality of node C with respect to nodes A and I? (show your work)

Degree Centralization

Compute the degree centralization of the graph shown in Figure 1.