topological coefficient

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Feb 6, 2019, 11:38:23 PM2/6/19

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Hello,

I am trying to run through the formula to calculate topological coefficients from:

Equation:

T_n = avg ( J(n,m) ) / k_n.

Even on the very simple 5 node network I am having a very hard time calculating the topological coefficients with confidence.

Is there pseudo code anywhere to help guide me through it, I am just not understanding it (below are some attempts at what I think is happening).

For example on node C:

T_c = avg( J(c,b) , J(c,d), J(c,e), J(c,a)) / k_c

J(c,b) = 1 (they share D) + 1 (connected) = 2

J(c,d) = 2 (they share B, C) + 1 (connected) = 3

J(c,e) = 1 (they share D) + 1 (connected) = 2

J(c,a) = 1 (they share B) + 0 (not connected) = 1

avg( J(c,b) , J(c,d), J(c,e), J(c,a)) = ((2+3+2+1)/ 4) = 2

k_c = 3 (degrees)

T_c = 2/3

T_b = avg( J(b,a) , J(b,c), J(b,d), J(b,e)) / k_b

J(b,a) = 0 (A only has 1 neighbor) <-- divided by 3 because J(b,a) not in the picture

J(b,c) = 1 (they share D) + 1 (they are connected) = 2

J(b,d) = 1 (they share C) + 1 (they are connected) = 2

J(b,e) = 2 (they share C,D) + 0 (they are not connected) = 2

avg(J(b,a) , J(b,c), J(b,d), J(b,e)) = ((0+2+2+2)/ 3) = 2

k_b = 3 (degrees)

T_b = 2/3

For example on node E:

T_e = avg( J(e,c) , J(e,d), J(e,b), J(e,a)) / k_e

J(e,c) = 1 (they share D) + 1 (connected) = 2

J(e,d) = 1 (they share C) + 1 (connected) = 2

J(e,b) = 2 (they share C, D) + 0 (not connected) = 2

J(e,a) = 0 (they share nothing) + 0 (not connected) = 0

avg( J(e,c) , J(e,d), J(e,b), J(e,a)) = ((2+2+2+0) / 3) = 2 . <-- divided by 3 because J(e,a) not in the picture

k_e = 2

T_e = 2/2

Is this the proper way of doing it?

Screen Shot 2019-02-06 at 8.14.28 PM.png

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Feb 7, 2019, 9:46:35 AM2/7/19

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It certainly looks correct to me, and it corresponds to the values that NetworkAnalyzer spits out...