#!/usr/bin/env python
# coding: utf-8

# # Page Rank and HITS

# In[1]:


import numpy as np
import matplotlib.pyplot as plt
plt.xkcd()
import networkx as nx
get_ipython().run_line_magic('matplotlib', 'inline')


# During with lab we will check the change of results of Page Rank and HITS algorithms with respect to the values of $\alpha$ and number of iterations.

# ### Task 1.

# a) Firstly let's make experiment for small network (Zachary or any other small one). Set any 3 distinct values for $\alpha$, fix the number of iterations, and run Page Rank. Plot results PR values wrt $\alpha$

# In[2]:


G = nx.karate_club_graph()
# Continue here
# Explain the results

fig = plt.figure(1, figsize=(7,7))
ax = plt.subplot(111)

alphas = np.arange(0.1, 0.9, 0.2)

for alp in alphas:
    pr = nx.pagerank(G, alpha=alp)
    prval = pr.values()
    ax.plot(prval, c=np.random.rand(3,1), label='alpha {0:.2f}'.format(alp))
    
ax.legend()

    


# In[3]:


nx.draw(G)


# b) Do the same for the number of iterations

# In[4]:


# Continue here


# c) Plot Page-Rank vs. Degree centrality

# In[5]:


# Continue here
pr = nx.pagerank(G, alpha=0.8)
pr = pr.values()
d = nx.degree_centrality(G)
d = d.values()

plt.plot(d, pr, '*')
plt.xlabel('Degree Centrality')
plt.ylabel('Page-Rank')


# ### Task 2.

# Let's switch to a bigger network. Download [political blogs](http://networkdata.ics.uci.edu/data/polblogs/polblogs.gml) network. Check its basic properties. Run HITS algorithm. Try to inverstigate the top nodes.

# In[6]:


# Continue here
# 
G = nx.read_gml('polblogs.gml')


# In[7]:


G.is_directed()
A = nx.adjacency_matrix(G)

P = nx.DiGraph(A)


# In[8]:


(h, a) = nx.hits(P)
a = a.values()
h = h.values()


# In[9]:


plt.plot(h,a, '*')
plt.xlabel('Hubs')
plt.ylabel('Auth')


# In[10]:


idx = np.argsort(a)
idx[-3]


# In[11]:


G.node[54]