Social Network Analysis is one of the important topics of Machine Learning. A basic step for social network analysis is to encode the data into low dimensional representations.
Social networks have greatly facilitated communication between web users around the world.
The social network analysis helps summarizing the interests and opinions of users, discovering patterns from the interactions between users, and mining the events that take place in online platforms.
In this Article I will explain you social network analysis with machine learning, and then we will create a network between the users of Facebook all around the world.
Lets start this task by importing the libraries
# for some basic operations import numpy as np import pandas as pd # for basic visualizations import matplotlib.pyplot as plt import seaborn as sns # for network visualizations import networkx as nx
Getting Started with the Types of Networks Graph
1. Undirected Graphs
g = nx.Graph()
g.add_edge('A', 'B')
g.add_edge('B', 'C')
g.add_edge('C', 'D')
g.add_edge('B', 'D')
g.add_edge('A', 'E')
g.add_edge('A', 'F')
g.add_edge('A', 'G')
import warnings
warnings.filterwarnings('ignore')
plt.rcParams['figure.figsize'] = (10, 10)
plt.style.use('fivethirtyeight')
pos = nx.spring_layout(g)
# drawing nodes
nx.draw_networkx_nodes(g, pos, node_size = 900, node_color = 'orange')
# drawing edges
nx.draw_networkx_edges(g, pos, width = 6, alpha = 0.5, edge_color = 'black')
# labels
nx.draw_networkx_labels(g, pos, font_size = 20, font_family = 'sans-serif')
plt.title('Undirected Graphs', fontsize = 20)
plt.axis('off')
plt.show()
An undirected graph is graph, i.e., a set of objects that are connected together, where all the edges are bidirectional.
An undirected graph is sometimes called an undirected network. In contrast, a graph where the edges point in a direction is called a directed graph.
2. Directed Graphs
g = nx.DiGraph()
g.add_edge('A', 'B')
g.add_edge('B', 'C')
g.add_edge('C', 'H')
g.add_edge('B', 'D')
g.add_edge('A', 'E')
g.add_edge('A', 'F')
g.add_edge('A', 'G')
import warnings
warnings.filterwarnings('ignore')
plt.rcParams['figure.figsize'] = (10, 10)
plt.style.use('fivethirtyeight')
pos = nx.spring_layout(g)
# drawing nodes
nx.draw_networkx_nodes(g, pos, node_size = 900, node_color = 'yellow')
# drawing edges
nx.draw_networkx_edges(g, pos, edge_color = 'brown', width = 6, alpha = 0.5)
# defining labels
nx.draw_networkx_labels(g, pos, font_size=20, font_family='sans-serif')
plt.title('Directed Graphs', fontsize = 20)
plt.axis('off')
plt.show()
A directed graph is graph, i.e., a set of objects that are connected together, where all the edges are directed from one vertex to another. A directed graph is sometimes called a digraph or a directed network.
3. Weighted networks Graph
g = nx.Graph()
g.add_edge('A', 'B', weight = 8)
g.add_edge('B', 'C', weight = 12)
g.add_edge('C', 'J', weight = 15)
g.add_edge('B', 'D', weight = 3)
g.add_edge('A', 'E', weight = 5)
g.add_edge('A', 'F', weight = 18)
g.add_edge('A', 'G', weight = 10)
import warnings
warnings.filterwarnings('ignore')
plt.rcParams['figure.figsize'] = (10, 10)
plt.style.use('fivethirtyeight')
plt.title('Weighted Networks', fontsize = 20)
elarge = [(u, v) for (u, v, d) in g.edges(data=True) if d['weight'] < 10]
esmall = [(u, v) for (u, v, d) in g.edges(data=True) if d['weight'] >= 10]
pos = nx.spring_layout(g)
# nodes
nx.draw_networkx_nodes(g, pos, node_size = 900, node_color = 'pink')
# edges
nx.draw_networkx_edges(g, pos, edgelist = elarge, width = 6)
nx.draw_networkx_edges(g, pos, edgelist = esmall, width = 6, alpha = 0.5, edge_color = 'b', style = 'dashed')
# labels
nx.draw_networkx_labels(g, pos, font_size = 20, font_family = 'sans-serif')
plt.axis('off')
plt.show()
A weighted graph is a graph in which each branch is given a numerical weight. A weighted graph is therefore a special type of labeled graph in which the labels are numbers (which are usually taken to be positive).
4. Signed networks graph
g = nx.Graph()
g.add_edge('A', 'B', sign = '+')
g.add_edge('B', 'C', sign = '-')
g.add_edge('C', 'J', sign = '+')
g.add_edge('B', 'D', sign = '-')
g.add_edge('A', 'E', sign = '+')
g.add_edge('A', 'F', sign = '+')
g.add_edge('A', 'G', sign = '-')
import warnings
warnings.filterwarnings('ignore')
plt.rcParams['figure.figsize'] = (10, 10)
plt.style.use('fivethirtyeight')
plt.title('Signed Networks', fontsize = 20)
elarge = [(u, v) for (u, v, d) in g.edges(data=True) if d['sign'] == '+']
esmall = [(u, v) for (u, v, d) in g.edges(data=True) if d['sign'] == '-']
pos = nx.spring_layout(g)
# nodes
nx.draw_networkx_nodes(g, pos, node_size=700)
# edges
nx.draw_networkx_edges(g, pos, edgelist=elarge,
width=6)
nx.draw_networkx_edges(g, pos, edgelist=esmall,
width=6, alpha=0.5, edge_color='b', style='dashed')
# labels
nx.draw_networkx_labels(g, pos, font_size=20, font_family='sans-serif')
plt.axis('off')
plt.show()
In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive.
5. Relation networks graph
g = nx.Graph()
g.add_edge('A', 'B', relation = 'family')
g.add_edge('B', 'C', relation = 'friend')
g.add_edge('C', 'J', relation = 'coworker')
g.add_edge('B', 'D', relation = 'family')
g.add_edge('A', 'E', relation = 'friend')
g.add_edge('A', 'F', relation = 'coworker')
g.add_edge('A', 'G', relation = 'friend')
import warnings
warnings.filterwarnings('ignore')
plt.rcParams['figure.figsize'] = (10, 10)
plt.style.use('fivethirtyeight')
plt.title('Relation based Networks', fontsize = 20)
pos = nx.spring_layout(g)
# nodes
nx.draw_networkx_nodes(g, pos, node_size = 700, node_color = 'lightgreen')
# edges
nx.draw_networkx_edges(g, pos, width = 6, alpha = 0.5, edge_color = 'black')
# labels
nx.draw_networkx_labels(g, pos, font_size = 20, font_family = 'sans-serif')
plt.axis('off')
plt.show()
Checking the different types of Layouts available in Networks
# See what layouts are available in networkX
[x for x in nx.__dir__() if x.endswith('_layout')]['bipartite_layout', 'circular_layout', 'kamada_kawai_layout', 'random_layout', 'rescale_layout', 'shell_layout', 'spring_layout', 'spectral_layout', 'planar_layout', 'fruchterman_reingold_layout', 'spiral_layout']
Bipartite Network graphs
from networkx.algorithms import bipartite
B = nx.Graph()
B.add_nodes_from(['A','B','C','D','E'], bipartite = 0)
B.add_nodes_from([1, 2, 3, 4], bipartite = 1)
B.add_edges_from([('A', 1),('B', 1),('C', 1),('C', 3),('D', 2),('E',3),('E',4)])
import warnings
warnings.filterwarnings('ignore')
plt.rcParams['figure.figsize'] = (10, 10)
plt.style.use('fivethirtyeight')
plt.title('Bi-Partite Networks', fontsize = 20)
pos = nx.shell_layout(B)
# nodes
nx.draw_networkx_nodes(B, pos, node_size = 700, node_color = 'lightblue')
# edges
nx.draw_networkx_edges(B, pos, width = 6, alpha = 0.5, edge_color = 'black')
# labels
nx.draw_networkx_labels(B, pos, font_size = 20, font_family = 'sans-serif')
plt.axis('off')
plt.show()
In the mathematical field of graph theory, a bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets and such that every edge connects a vertex in to one in.
Vertex sets and are usually called the parts of the graph.
Projected Network graphs
B = nx.Graph()
B.add_edges_from([('A', 1),('B', 1),('C', 1),('D', 1),('H', 1),('B', 2),('C', 2),('D', 1),
('H', 1),('B', 2),('C', 2),('D', 2),('E', 2),('G', 2),('E', 3),('F', 3),
('H', 3), ('J', 3), ('E', 4), ('I',4), ('J', 4)])
X = set(['A','B','C','D','E','F','G','H','I','J'])
P = bipartite.projected_graph(B, X)
pos = nx.circular_layout(P)
nx.draw_networkx_nodes(P, pos, node_color = 'cyan')
nx.draw_networkx_edges(P, pos, edge_color = 'magenta', width = 6, alpha = 0.5)
nx.draw_networkx_labels(P, pos, font_size = 20, font_family = 'sans-serif')
plt.title('Projected Graph', fontsize = 20)
plt.axis('off')
plt.show()
Breadth-first search
Breadth-first search is an algorithm for traversing or searching tree or graph data structures.
It starts at the tree root, and explores all of the neighbor nodes at the present depth prior to moving on to the nodes at the next depth level.
a = nx.Graph()
a.add_edge('A', 'B')
a.add_edge('A', 'K')
a.add_edge('B', 'C')
a.add_edge('C', 'F')
a.add_edge('F', 'E')
a.add_edge('F', 'G')
a.add_edge('C', 'E')
a.add_edge('E', 'D')
a.add_edge('E', 'H')
a.add_edge('K', 'B')
a.add_edge('E', 'I')
a.add_edge('I', 'J')
a = nx.bfs_tree(a, 'A')
pos = nx.kamada_kawai_layout(a)
nx.draw_networkx(a, size = 900)
plt.axis('off')
plt.title('BFS Tree')
plt.show()
Random Geometric Network Graph
import matplotlib.pyplot as plt
import networkx as nx
G = nx.random_geometric_graph(200, 0.125)
# position is stored as node attribute data for random_geometric_graph
pos = nx.get_node_attributes(G, 'pos')
# find node near center (0.5,0.5)
dmin = 1
ncenter = 0
for n in pos:
x, y = pos[n]
d = (x - 0.5)**2 + (y - 0.5)**2
if d < dmin:
ncenter = n
dmin = d
# color by path length from node near center
p = dict(nx.single_source_shortest_path_length(G, ncenter))
plt.rcParams['figure.figsize'] = (10, 10)
nx.draw_networkx_edges(G, pos, nodelist=[ncenter], alpha=0.4)
nx.draw_networkx_nodes(G, pos, nodelist=list(p.keys()),
node_size=80,
node_color=list(p.values()),
cmap=plt.cm.Reds_r)
plt.title('Random Geometric Graph', fontsize = 20)
plt.xlim(-0.05, 1.05)
plt.ylim(-0.05, 1.05)
plt.axis('off')
plt.show()
Karate Club Networks
import matplotlib.pyplot as plt
import networkx as nx
G = nx.karate_club_graph()
plt.style.use('fivethirtyeight')
nx.draw_circular(G, with_labels=True)
plt.title(' Karate Club Networks')
plt.show()Facebook Social Network Analysis
Now lets create a Facebook social media network using the Facebook data set and Machine learning.
Download the data set
Reading the data set
fb = nx.read_edgelist('facebook.txt', create_using = nx.Graph(), nodetype = int)print(nx.info(fb))
Name: Type: Graph Number of nodes: 4039 Number of edges: 88234 Average degree: 43.6910
pos = nx.spring_layout(fb)
import warnings
warnings.filterwarnings('ignore')
plt.style.use('fivethirtyeight')
plt.rcParams['figure.figsize'] = (20, 15)
plt.axis('off')
nx.draw_networkx(fb, pos, with_labels = False, node_size = 35)
plt.show()
# checking the betweenness centrality bc = nx.betweenness_centrality(fb) bc
# checking the degree of each node in the network degree = nx.degree_histogram(fb) degree
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