Fatman Evolutionary Model in Social Networks

Prerequisite: Introduction to Social Networks

In the Fatman evolutionary model, there are 3 main concepts to make an evolutionary model i.e Homophily, Social influence, and closure.

1. Homophily- People who are similar to each other, they tend to make friends with each other.
2. Social Influence- People change their behavior and properties because of social influence.
3. Closure-  There are 3 main kinds of closures i.e. triadic closure, membership closure, and foci closure.

• Triadic closure- In triadic closure, if A is a friend of B and B is a friend of C then C will eventually become friends of A.
• Membership closure- In membership closure if A is a friend of B and A is a member of a club then there is a tendency that B will join the same club.
• Foci closure- It is the probability of becoming friends when they have the same foci. In membership closure, if A and B are in the same club then there is a tendency that they will become friends.

So, According to Fatman Hypothesis, beware of fat friends, if your friend is fat then the probability of you gaining the weight becomes high.

Now the below code will show you the implementation of the above 3 concepts using the evolutionary model in python by taking an example.

Assume there is a city with a number of people, and we have everyone’s BMI. Then we will see as evolution continues people having similar BMI become friends to each other which is Homophily. Then we will create some foci like Gym etc. and see how eventually people with similar foci become a friend and then we will implement social foci. 

Algorithm:

1. Create a graph with say N nodes,
2. Add edges and labels for each node.
3. Now add social foci and social foci label for each node
4. .Now implement homophily.
5. After that implement closure.
6. At last implement social influence.
7. Now Visualize the graph.

Python Code for Fatman Evolutionary Model:

Python3

import networkx as nx
import matplotlib.pyplot as plt
import random
import math

# 1- Create a graph with lets say 100 nodes
# 2- Add edges and labels.
def create():
    G = nx.Graph()
    G.add_nodes_from(range(1, 101))
    return G


def visualize(G):
    labeldict = get_labels(G)
    nodesize = get_size(G)
    color = get_colors(G)
    nx.draw(G, labels=labeldict, node_size=nodesize, node_color=color)
    plt.show()


def assign_bmi(G):

    for each in G.nodes():
        G.nodes[each]['name'] = random.randint(15, 40)
        G.nodes[each]['type'] = 'person'


def get_labels(G):
    dict1 = {}

    for each in G.nodes():
        dict1[each] = G.nodes[each]['name']

    return dict1


def get_size(G):
    array1 = []
    for each in G.nodes():
        if (G.nodes[each]['type'] == 'person'):
            array1.append(G.nodes[each]['name'] * 20)
        else:
            array1.append(500)
    return array1

# 3. Add foci nodes
def add_foci_nodes(G):
    n = G.number_of_nodes()
    i = n + 1
    foci_nodes = ['gym', 'eatout', 'movie_club',
                  'karate_club', 'yoga_club']

    for j in range(5):
        G.add_node(i)
        G.nodes[i]['name'] = foci_nodes[j]
        G.nodes[i]['type'] = 'foci'
        i += 1


def get_colors(G):
    c = []

    for i in G.nodes():
        if (G.nodes[i]['type'] == 'person'):
            if (G.nodes[i]['name'] == 15):
                c.append('yellow')
            elif (G.nodes[i]['name'] == 40):
                c.append('green')
            else:
                c.append('blue')
        else:
            c.append('red')
    return c


def get_person_nodes(G):
    p = []

    for i in G.nodes():
        if (G.nodes[i]['type'] == 'person'):
            p.append(i)
    return p


def get_foci_nodes(G):
    f = []

    for i in G.nodes():
        if (G.nodes[i]['type'] == 'foci'):
            f.append(i)
    return f


def add_foci_edges(G):
    foci_nodes = get_foci_nodes(G)
    person_nodes = get_person_nodes(G)

    for i in person_nodes:
        r = random.choice(foci_nodes)
        G.add_edge(i, r)

# 4. Implement Homophily
def homophily(G):
    pnodes = get_person_nodes(G)

    for u in pnodes:
        for v in pnodes:
            if (u != v):
                diff = abs(G.nodes[u]['name'] - G.nodes[v]['name'])
                p = 1 / (diff + 1000)
                r = random.uniform(0, 1)
                if (r < p):
                    G.add_edge(u, v)

# 5. Implement Closure
def common(u, v, G):
    nu = set(G.neighbors(u))
    nv = set(G.neighbors(v))
    return (len(nu & nv))


def closure(G):
    array1 = []
    for u in G.nodes():
        for v in G.nodes():
            if (u != v and G.nodes[u]['type'] == 'person' or G.nodes[v]['type'] == 'person'):

                # common function will return start node,
                # end node and Graph itself.
                k = common(u, v, G)
                p = 1 - math.pow(1 - 0.01, k)
                tmp = []
                tmp.append(u)
                tmp.append(v)
                tmp.append(p)
                array1.append(tmp)
    for i in array1:
        u = i[0]
        v = i[1]
        p = i[2]
        r = random.uniform(0, 1)
        if r < p:
            G.add_edge(u, v)

# 6. Implement Social Influence
def social_influence(G):
    fnodes = get_foci_nodes(G)

    for i in fnodes:
        if (G.nodes[i]['name'] == 'eatout'):
            for j in G.neighbors(i):
                if (G.nodes[j]['name'] != 40):
                    G.nodes[j]['name'] = G.nodes[j]['name'] + 1

        if (G.nodes[i]['name'] == 'gym'):
            for j in G.neighbors(i):
                if (G.nodes[j]['name'] != 15):
                    G.nodes[j]['name'] = G.nodes[j]['name'] - 1


G = create()
assign_bmi(G)

# to add foci field in the nodes
add_foci_nodes(G)
add_foci_edges(G)
visualize(G)

for t in range(1, 3):
    homophily(G)
    visualize(G)
    closure(G)
    visualize(G)
    social_influence(G)
    visualize(G)

Output:

The output contains graphs having homophily, closure, and change in behavior i.e. social influence.