1. Point centrality:

Point centrality measures how centrally a point is located in a given graph. Usually the point at the center of a star or the hub of a wheel is the most central possible position. There are three approaches to measuring the point centrality:

1) Point centrality based on the degree: the point with the largest degree is the most central point in the graph.

Nieminen's (1974) measurement: count of the degree or number
of adjacencies, for a point p_{k}:

where n = number of points

a(p_{i},p_{k})=1 if and only if pi
and p_{k} are connected by a line

0 otherwise

If we control the size of the graph by dividing C_{D}(p_{k})
by n-1, which is the maximum degree of p_{k} in any graph,
and make the measurement comparable between graph, we get a "relative
centrality" for p_{k}, C'_{D}(p_{k}).

2) Point centrality based on betweenness: the point which falls
on the largest numbers of geodesic paths (that is, the shortest
path link a given pair, say, p_{i} and p_{j})
between pairs is the most central point in the graph.

The measurement developed by Anthonisse (1971) and Freeman (1977):

where g_{ij} = the number of geodesics linking p_{i}
and p_{j}.

g_{ij}(p_{k})= the number of geodesics
linking pi and p_{j} that contain p_{k}.

Like the centrality based on the degree, we divide C_{B}(p_{k})
by the maximum value in any graph, (n-2)(n-1)/2 =(n2-3n+2)/2,
to get a "relative centrality" based on betweenness
for p_{k}, C'_{B}(p_{k}).

3)Point centrality based on closeness: the point which is closest to all other points in the graph is the most central point.

Sabidussi's (1966) measurement:

where d(p_{i},p_{k}) = the number of edges in
the geodesic linking pi and p_{k}.

The "relative centrality" based on closeness is:

Different research interests leads to different measurement:
Concern with communication activity suggests a degree-based measure.
Interest in control of communication requires a measure based
upon betweenness. And concern with either independence or efficiency
leads to the choice of a measure based upon closeness.

2. Graph centrality (the centralization of the network): measures the differences between the centrality of the most central point and that of all others. The larger the relative differences are ( controlling for the size of the graph), the more central a graph (network) is.

The general formula for graph centrality is:

where n=number of points

C_{X}(p_{i}) = one of the point centralities
defined above

C_{X}(p*) = largest value of CX(pi) for any point in
the network and

= the maximum possible sum of differences in

point centrality for a graph of n points.

(Note: Since C_{X} is a ratio of an observed sum of differences
to its maximum value, it will vary between 0 and 1.)