Graphics Reference
In-Depth Information
Centrality
Centrality
is an attempt to identify the nodes at the center of the graph.
You can measure centrality in many different ways:
•
Degree centrality
is the simplest. This is simply the node with the
highest degree (that is, the highest number of connections). In a social
network, this is the very well-connected person, and the importance of
this person is that he or she will likely know what's going on around him
or her because he or she is so well-connected.
•
Betweenness centrality
measures the number of times that a
particular node is a member of the shortest path between two other
nodes.
•
Closeness centrality
measures the average distance to all other nodes
from each node. In a social network, this could be a VIP for which all
communications pass through a few intermediaries (for example, an
assistant or a spouse), but acts as a bridge between different clusters.
•
Katz centrality
sums all of the weighted distances to all other nodes
from a given node. The further away a node is from the measured node,
the lower the weight and the lower the contribution to centrality.
•
Eigenvector
centrality is similar to Katz centrality, but it is a recursive
approach where a node is more likely to be central if its neighbors are
central.
•
PageRank
centrality is famous as the method used by Google to rank
pages. Similar to Katz and eigenvector, it additionally weights nodes by
other factors, such as the degree of the node.
So, is Kevin Bacon at the center of all actors? Perhaps Bacon has starred in a
large number of epic movies with casts of thousands and, therefore, has the
highest degree resulting in degree centrality. Or, perhaps Bacon has been
in only a few movies but is connected with some extremely well-connected
actors for betweenness centrality. The answer also depends on the data.
With each new movie, every actor's centrality score can shift.
These subtle differences can be important when discussing relative
importance of different nodes in a network, as shown in the diagrammatic
social network in
Figure 4-4
.
