An important form of Zipf\'s law is the citation patterns found in scientific ar

Question

An important form of Zipf's law is the citation patterns found in scientific articles. Rather than doing equations, let's make a simulation of a simplified version of this. (a) Start with a list containing the integers 1 and 2. (b) Choose one number randomly from the list and append it back to the list. You can use the sample() function from the random module to do this. (c) Append the next number (3) to the list. (d) Repeat these last two steps 1,000 times, incrementing the new number each time until you get a list of 2,002 integers. Now, count up how many times each integer appears in the list and plot a rank-value plot on a log-log scale. Explain how we know that the plot exhibits a power-law scaling, and approximate the scaling exponent.

Explanation / Answer

import java.util.ArrayList;
import java.util.Collections;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Random;
import java.util.Set;
import java.util.TreeMap;

public class ZipfLaw {
  
   public static void main(String[] args) {
      
       //Initializing list and map of integer
       List<Integer> list=new ArrayList<Integer>();
       Map<Integer,Integer> map=new TreeMap<Integer,Integer>();
      
       //Intially adding two numbers in list 1 and 2
       list.add(1);
       list.add(2);
       Random rand = new Random();
       int num;
      
       //Getting random number bounded with value 2002 and appending in list
       for(int i=0;i<1000;i++){
           num=rand.nextInt(2002);
           list.add(num);          
       }
      
       //Initializing set of integer so for the purpose of removing duplicates from list
       Set<Integer> set=new HashSet<Integer>(list);
       int number=0;
       int frequency=0;
      
       Iterator<Integer> it=set.iterator();
      
       //calculating frequency of the number and putting in TreeMap so it can be auto sorted in ascending order
       while(it.hasNext()){
          
           number=it.next();
           frequency=Collections.frequency(list, number);
           map.put(number, frequency);
          
       }
       //in map key is random number and value as frequency of the number
       //Displaying key value pair of random number as key and its frequency as value
       System.out.println(map);
      
   }

}

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