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Centrality MeasuresThese measure a nodes importance or
prominence in the network.
The more central a node is in a network the more significant it
is to aidin the spread of infection.
Walk: A walk is a sequence of nodes connected by edges.
Path: A path is a walk with no repeated nodes.
Geodesic: This is the shortest path between two nodes.
Distance: This is the length of the shortest path between two
nodes.
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Degree: The degree of a vertex is the number of other vertices
to which it isattached.
Normalized Degree (nDegree): Is the degree divided by the
maximumpossible degree expressed as a percentage.
Degree nDegree
------------ ------------
1 3.000 75.000
4 3.000 75.000
3 3.000 75.000
2 2.000 50.000
5 1.000 25.000
Farness: This is the sum of the lengths of the geodesics to
every other node .
(i.e. the sum of the distances to every other every other
node).
Closeness: The reciprocal of farness is closeness.
Normalized Closeness (nCloseness): Is the closeness divided by
the minimumpossible farness expressed as a percentage.
nCloseness
------------
1 80.000
2 57.143
3 80.000
4 80.000
5 50.000
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Eigenvector: The equation Mx = x can be viewed as a linear
transformationthat maps a given vector x into a new vectorx, where
M is the adjacencymatrix. The nonzero solutions of the equation
that are obtained by using a
value of
(known as an eigenvalue) are called the eigenvectors
correspondingto that eigenvalue.
Normalized Eigenvector (nEigenvector): This is the eigenvector
divided by
the maximum difference possible expressed as a percentage.
Betweenness: This is a measure of the number of times a node
occurs on a
geodesic. So, to have a large betweenness centrality, the node
must be betweenmany of the nodes via their geodesics.
Normalized Betweenness (nBetweenness): Is the betweenness
divided by the
maximum possible betweenness expressed as a percentage.
nBetweenness nEigenvector
------------ ------------
1 16.667 75.954
2 0.000 57.515
3 16.667 75.954
4 50.000 67.140
5 0.000 25.420
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CorrelationA high correlation tells us there may be an easier
way of measuring the
centalities on a larger scale project.
For instance, measuring the degree of a farm by observing that
farm is much
easier than measuring its betweenness or closeness, as we would
then have to
observe the entire network of farms. So, if measuring degree
means we can
make assumptions about the values of another centrality then
this saves us
measuring both centralities. This is providing that we are not
essentially
measuring the same thing which would inevitably give a high
correlation.
Assortative Random 1 Random 2 Random 3 Scale-FreenDegree v
nCloseness 0.2299 0.9731 0.9531 0.9335 0.8557
nDegree v nBetweenness 0.1461 0.6224 0.7443 0.6791 0.8954
nDegree v nEigenvector 0.9242 0.9673 0.9505 0.9415 0.9352
nCloseness v nBetweenness 0.2466 0.6094 0.6281 0.6628 0.7565
nCloseness v nEigenvector 0.3317 0.9431 0.9554 0.8766 0.9478
nBetweenness v nEigenvector 0.1316 0.4576 0.5464 0.467
0.7694
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Random
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Scale-free
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Assortative
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Lattice
