An office local network has two servers and and a switch that connects to both

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

Many Parts, One Behaviour, Ch Networks as graphs: degree, distance and clustering

Problem

An office local network has two servers

A

and

C

and a switch

B

that connects to both, with

A

and

C

also linked directly to each other, so that

A,B,C

form a triangle. Two workstations

D

and

E

plug only into the switch

B

and have no other link. Treat the wiring as a simple, undirected, unweighted network. ((a)) Write the

5\times5

adjacency matrix (order

A,B,C,D,E

), give the degrees and the mean degree. ((b)) Give the degree distribution

p_k

and the heterogeneity ratio

\langle k^2\rangle/\langle k\rangle^2

. ((c)) Compute the clustering coefficient

C

. ((d)) Starting from

\mathbf x^{(0)}=(1,1,1,1,1)

, apply the adjacency matrix twice and report the ratio of

B

's score to

D

's score.

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