Lecture 11 Network Analysis (2)

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Lecture 11 Network Analysis (2)

• 11-1 Evaluation of network structure ? Index
• Relative complexity and connectivity can be
  evaluated in several ways (? and a).
• The ? index is defined as the ratio of the actual
  number of links to the maximum possible number of
  links in a network.

Left example Actual links 4 Maximum possible
number of links - 6
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11-1 Evaluation of Network Structure ? Index
(Cont.)

• A graph is planar if it can be drawn in a plane
  without graph edges crossing. In a planar graph,
  the maximum number of links is always equal to
  3(n-2). n number of nodes.

The value of the ? index ranges between 0 and 1.
A value closer to 0 indicates? Closer to 1?
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11-1 Evaluation of Network Structure ? Index
(Cont.)
For non-planar graphs (such as airline
transportation), the maximum number of links is
equal to n(n-1)/2.
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11-2 Evaluation of Network Structure a Index
The a index is defined as the ratio of the actual
number of circuits to the maximum number of
circuits in the network. Circuit A circuit is a
loop in the network. When a loop exists, each
node has two ways to reach any other node in the
network.
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11-2 Evaluation of Network Structure a Index
(Cont.)
Graph (network) ABCD has 4 nodes. Maximum loop
number is 3. a value is 1/3. Question How many
ways you can go from A to C?
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11-2 Evaluation of Network Structure a Index
(Cont.)
The a value evaluates network structure in terms
of the number of ways you can proceed from one
node to another. In general A better developed
transportation networklt-gthigher values on both a
and ? lt-gthigher levels of complexity and
connectivity.
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11-3 Network Diameter
The diameter of a network represents the maximum
number of steps required to move from any node to
any other node through the shortest possible
routes within a connected network.
Diameter of the left graph is 3