''' 
Social network

As you might imagine from the experience of the recent years, modelling an 
epidemic spread is rather useful. One of the possible models is the so-called 
"probabilistic network model", in which we model pathogen spread in the group 
via a network of social contacts. As it turns out, a social network can 
conveniently be represented by a matrix W. Let's look at an example:

W = [ 1 1 0 ]
    [ 1 1 1 ]
    [ 0 1 1 ]

You can imagine each row and each column representing a person. Our example 
matrix W therefore outlines a social network of 3 people. When two individuals 
know each other, the corresponding element in the matrix is 1. In matrix 
terminology, we can say that element w_ij = 1 when persons i and j know each 
other. The matrix is also symmetrical, i.e., w_ij = w_ji. If w_ii = 1, then i 
abides by Socrate's advice: "know thyself".

Remember: in w_ij, i denotes the row and j the column.

Below we give you a social network matrix W to use in the exercises. 
We also offer some general tips/hints to keep in mind:
- Matrix is symmetric, so (when applicable) make sure not to count the same 
contact twice.
- When looking at contacts between differet individuals, you can exclude 
elements from matrix diagonal (i.e., the "know thyself" elements).
- Remember good coding practices and avoid hardcoding. Your code should work 
for any social network matrix.
'''

import numpy as np

# Define social network matrix
num_people = 20 # Matrix of 20 people
np.random.seed(0) # Setting seed for random number generation for reproducibility
W = np.random.choice([0, 1], size=(num_people, num_people), p=[0.6, 0.4])
np.fill_diagonal(W, 1) # Set diagonal elements to 1


'''
Exercise A: Person number 5

How many contacts does person number 5 have? Use Python to find the answer and 
print it.

Hint: How does counting in Python work?
'''

# Your code here


'''
Exercise B: The influencer

Find out which person in your social network has the most contacts (i.e., 
who's the influencer)? Make a print statement about it.
'''

# Your code here


'''
Exercise C: Interconnectedness

How many social contacts in total are represented in W? Calculate and make 
a print statement.
'''

# Your code here


'''
Exercise D: A new friendship

Two people have met at a party, so now they also know each other. Make a new 
social network matrix W_new that also contains this contact.
In practice, identify two people in your matrix W that have not known each 
other (w_ij = 0) and turn the corresponding matrix element(s) to 1.

Is the influecer still the same person? You can reuse your code from above to 
find out.
'''

# Your code here