# probability

Introduction

Consider a network of N red and N bluish nodes. The presumption that there is a incorporate betwixt nodes of

identical varnish is p and the presumption that there is a incorporate betwixt nodes of contrariant varnish is q (p+q = 1).

If p > q, the nodes present a i-aim to conjoin to nodes of the selfselfidentical varnish. For q = 0 the network has

at lowest two components, containing nodes after a while the selfselfidentical varnish.

The learner is requested to utensil a command which simulates a qualified Barabasi-Albert yield to

the subjoined workflow:

1. Create a root network moored of 4 bluish nodes and 4 red nodes

2. At each season march add a new node. Its varnish is randomly clarified depending on a parameter r

(0 ≤ r ≤ 1): if r = 0 all nodes gain be bluish, if r = 1 all nodes gain be red, interjacent estimates

gain detail contrariant percentages. For stance, if r = 0.1 solely 10% of nodes gain be red. Hint:

create a progression of N − 8 varnishs (red or bluish) compact after a while the clarified estimate of r

3. Depending on the estimate of p, and accordingly of q, each new node gain be conjoined to some nodes

of the selfselfidentical varnish and some others of the other varnish

4. When the network is adequate, accumulation the rate distribution

5. Plot the rate distributions identical to 4 contrariant estimates of p for a agricultural estimate of r

6. Plot the rate distributions identical to 4 contrariant estimates of r for a agricultural estimate of p

To do

1. Use Python 3

2. Use matplotlib for the plots

3. Choose a sufficiently liberal estimate of N (no toy networks)

4. N, p, r must be input parameters of the program Introduction

Consider a network of N red and N bluish nodes. The presumption that there is a incorporate betwixt nodes of

identical varnish is p and the presumption that there is a incorporate betwixt nodes of contrariant varnish is q (p+q = 1).

If p > q, the nodes present a i-aim to conjoin to nodes of the selfselfidentical varnish. For q = 0 the network has

at lowest two components, containing nodes after a while the selfselfidentical varnish.

The learner is requested to utensil a command which simulates a qualified Barabasi-Albert yield to

the subjoined workflow:

1. Create a root network moored of 4 bluish nodes and 4 red nodes

2. At each season march add a new node. Its varnish is randomly clarified depending on a parameter r

(0 ≤ r ≤ 1): if r = 0 all nodes gain be bluish, if r = 1 all nodes gain be red, interjacent estimates

gain detail contrariant percentages. For stance, if r = 0.1 solely 10% of nodes gain be red. Hint:

create a progression of N − 8 varnishs (red or bluish) compact after a while the clarified estimate of r

3. Depending on the estimate of p, and accordingly of q, each new node gain be conjoined to some nodes

of the selfselfidentical varnish and some others of the other varnish

4. When the network is adequate, accumulation the rate distribution

5. Plot the rate distributions identical to 4 contrariant estimates of p for a agricultural estimate of r

6. Plot the rate distributions identical to 4 contrariant estimates of r for a agricultural estimate of p

To do

1. Use Python 3

2. Use matplotlib for the plots

3. Choose a sufficiently liberal estimate of N (no toy networks)

4. N, p, r must be input parameters of the program

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