Friendship Network, Part II

# Import modules needed
import igraph
import numpy
import matplotlib.pyplot as plt
%matplotlib inline

hamsters = igraph.Graph.Read_GML('hamsterster_network.gml')

#compute degree list
hamsterDegreeList = hamsters.degree()

print "Degree of all nodes: ", hamsterDegreeList

#compute betweenness list
hamsterBetweennessList = hamsters.betweenness()

print "Betweenness of all nodes: ", hamsterBetweennessList

#compute Clustering Coefficient list
hamsterClusteringCoefficientList = hamsters.transitivity_local_undirected()

print "Clustering Coefficient List of all nodes: ", hamsterClusteringCoefficientList

# Use igraph to compute the density and diameter of the hamster network
hamsterDensity = hamsters.density()
hamsterDiameter = hamsters.diameter()

# Display the density and diameter of the graph
print "Graph density: ", hamsterDensity
print "Graph diameter: ", hamsterDiameter

# Compute number of components
hamsterConnectedComponents = len(hamsters.components())

print "The number of connected components in the hamster friendship network are: ", hamsterConnectedComponents

# Compute the average degree,betweenness,and clustering coefficient using lists made earlier to compute local properties

hamsterAvgDegree = numpy.mean(hamsterDegreeList)
print "The average degree of the friendship network is:", hamsterAvgDegree

hamsterAvgBetweenness = numpy.mean(hamsterBetweennessList)
print "The average betweenness of the friendship network is:", hamsterAvgBetweenness

hamsterAvgClusteringCoefficient = numpy.mean(hamsterClusteringCoefficientList)
print "The average clustering coefficient of the friendship network is:", hamsterAvgClusteringCoefficient

# Create a new plot that highlights the 
igraph.plot(hamsters, 
            layout = hamsters.layout_sugiyama(), 
            bbox=(750,600), 
            vertex_size=5,
            edge_size=.01)

# Visualize a histogram of the degree values for the Friendship network containing all degrees
plt.hist(hamsterDegreeList)
plt.title("Degree Histogram for Friendship Network")
plt.xlabel("Degree")
plt.ylabel("Frequency")
plt.show()

hamsterBetweennessList = hamsters.betweenness()
hamsterBetweennessList.sort()
hamsterBetweennessList.reverse()
max_betweennesses = []
max_betweennesses.append(hamsterBetweennessList[0])

for betweenness in hamsterBetweennessList:
    if (betweenness < max_betweennesses[0]):
            max_betweennesses.append(betweenness)
            break           
for betweenness in hamsterBetweennessList:
    if (betweenness < max_betweennesses[1]):
            max_betweennesses.append(betweenness)
            break            
print "The 3 highest betweenness values are:", (max_betweennesses)

count=0
for betweenness in hamsterBetweennessList:
    if (betweenness == max_betweennesses[0]):
            count= count+1
print "There are", count, "nodes with betweenness", max_betweennesses[0]

count=0
for betweenness in hamsterBetweennessList:
    if (betweenness == max_betweennesses[1]):
            count= count+1
print "There are", count, "nodes with betweenness", max_betweennesses[1]

count=0
for betweenness in hamsterBetweennessList:
    if (betweenness == max_betweennesses[2]):
            count= count+1            
print "There are", count, "nodes with betweenness", max_betweennesses[2]

hamsterClusteringCoefficientList = hamsters.transitivity_local_undirected()
hamsterClusteringCoefficientList = [x for x in hamsterClusteringCoefficientList if str(x) != 'nan']
hamsterClusteringCoefficientList.sort()
hamsterClusteringCoefficientList.reverse()

max_ClusteringCoefficient = []
max_ClusteringCoefficient.append(hamsterClusteringCoefficientList[0])

for ClusteringCoefficient in hamsterClusteringCoefficientList:
    if (ClusteringCoefficient < max_ClusteringCoefficient[0]):
        max_ClusteringCoefficient.append(ClusteringCoefficient)
        break           

for ClusteringCoefficient in hamsterClusteringCoefficientList :
    if (ClusteringCoefficient < max_ClusteringCoefficient[1]):
        max_ClusteringCoefficient.append(ClusteringCoefficient)
        break            
print "The 3 highest clustering coefficients are:", (max_ClusteringCoefficient)

count=0
for ClusteringCoefficient in hamsterClusteringCoefficientList:
    if (ClusteringCoefficient == max_ClusteringCoefficient[0]):
            count= count+1
print "There are", count, "nodes with clustering coefficient", max_ClusteringCoefficient[0]

count=0
for ClusteringCoefficient in hamsterClusteringCoefficientList:
    if (ClusteringCoefficient == max_ClusteringCoefficient[1]):
            count= count+1
print "There are", count, "nodes with clustering coefficient", max_ClusteringCoefficient[1]

count=0
for ClusteringCoefficient in hamsterClusteringCoefficientList:
    if (ClusteringCoefficient == max_ClusteringCoefficient[2]):
            count= count+1            
print "There are", count, "nodes with clustering coefficient", max_ClusteringCoefficient[2]   

#Hypothesis 1, finding highest degree via for loop
max_degree = 0
for number in hamsterDegreeList:
    if (number > max_degree):
        max_degree = number
print "The node with the highest degree has a degree of", max_degree

#Hypothesis 1, find the highest betweenness in the network via for loop
max_betweenness = 0
for number in hamsterBetweennessList:
    if (number > max_betweenness): 
        max_betweenness = number 
print "The node with highest betweeness has a betweenness of", max_betweenness

#Hypothesis 1, Here we are running a loop in the betweenness list but using the max degree node to see if its betweenness is the highest
for number in hamsterBetweennessList:
    if (number > max_degree):
        max_betweenness = number 
print "The betweenness of the node with the highest degree is", max_betweenness

hamsterDegreeList.remove(272)
print hamsterDegreeList

#We are calculating the new average degree from a list without a highest degree or 272
newhamsterAvgDegree = numpy.mean(hamsterDegreeList)
print "The average degree of the new friendship network, without highest degree 272, is:", newhamsterAvgDegree

#We are calculating the percent difference between the two average degrees 
hamster_diff = 13.35271944/13.491926803 

percent_difference = (1.0-hamster_diff)*100

print "The percentage difference of removing the hamster with the highest degree on the average degree is", percent_difference, "%"