Eight relay stations are linked as follows

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems

Many Parts, One Behaviour, Ch Communities: finding the groups in a network

Problem

Eight relay stations are linked as follows. Within group

X=\{1,2,3,4\}

: edges

1

2

1

3

2

3

3

4

. Within group

Y=\{5,6,7,8\}

: edges

5

6

6

7

7

8

5

8

. Between the groups: edges

4

5

2

6

3

7

. The network is simple and unweighted. ((a)) Write down the group labels

s_i=+1

for

i\in X

and

s_i=-1

for

i\in Y

, and use

R=\tfrac14\sum_{ij}A_{ij}(1-s_is_j)

to find the cut size of this bisection. ((b)) Check the result by counting the crossing edges directly.

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