03. Priority link model

"""
 Priority connection model ：

 A series of objects （ people ） Arrive one by one . The first arrival creates an entity . The following rules apply every time someone arrives ：
 In probability p（ smaller ） Under the circumstances , The new arrival creates a new entity ; In probability （1-p） Under the circumstances , New arrivals join an existing entity （ Generate links ）.
 The probability of adding a particular entity is equal to the size of the entity divided by the number of all arrivals so far .
"""

import random
import matplotlib.pyplot as plt


#  Initialize variable 
network = {0:[1]}
nodes = 1000
p = 0.1
num = 1

for i in range(1, nodes):
    network[i] = []
    x = random.random()
    accu_prob = 0.0
    num += 1 

    #  If the probability is less than the initial probability, a new entity will be created 
    if x <= p:
        network[i] = [1]
    else:
        #  On the contrary, it traverses value Calculate the probability of each entity 
        for key,value in network.items():
            accu_prob += len(value) / num
            if x <= accu_prob:
                network[key].append(1)
                break

node_list = [len(value) for value in network.values()]

plt.hist(node_list, 50)
plt.show()