A six-node network has a triangle (edges - , - , - )

PHYSICS · Subjective · 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

A six-node network has a triangle

\{1,2,3\}

(edges

1

2

1

3

2

3

), a path

4

5

6

among

\{4,5,6\}

(edges

4

5

5

6

), and a single bridge edge

3

4

joining the two parts. The network is simple and unweighted.Compute the modularity

Q=\sum_g\left[\dfrac{e_g}{M}-\left(\dfrac{d_g}{2M}\right)^2\right]

of the partition

\{1,2,3\}

against

\{4,5,6\}

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