Comportamiento en cascada en las redes sociales

Prerrequisito: Introducción a las Redes Sociales , Conceptos Básicos de Python 

Cuando las personas están conectadas en redes entre sí, pueden influir en el comportamiento y las decisiones de los demás. Esto se llama comportamiento en cascada en las redes.

Consideremos un ejemplo, supongamos que todas las personas en una sociedad han adoptado una tendencia X. Ahora viene una nueva tendencia Y y un pequeño grupo acepta esta nueva tendencia y después de esto, sus vecinos también aceptan esta tendencia Y y así sucesivamente.

Ejemplo de comportamiento en cascada (a = 2, b = 3 y p = 2/5)

Entonces, hay 4 ideas principales en Comportamientos en cascada:

1. Incrementando el pago.
2. Gente clave.
3. Impacto de las comunidades en las Cascadas.
4. Cascada y Clusters.

A continuación se muestra el código para cada idea.

1. Aumentar el pago.

# cascade pay off
import networkx as nx
import matplotlib.pyplot as plt
  
  
def set_all_B(G):
    for i in G.nodes():
        G.nodes[i]['action'] = 'B'
    return G
  
def set_A(G, list1):
    for i in list1:
        G.nodes[i]['action'] = 'A'
    return G
  
def get_colors(G):
    color = []
    for i in G.nodes():
        if (G.nodes[i]['action'] == 'B'):
            color.append('red')
        else:
            color.append('blue')
    return color
  
def recalculate(G):
    dict1 = {}
      
    # payoff(A)=a=4
    # payoff(B)=b=3
    a = 15
    b = 5
      
    for i in G.nodes():
        neigh = G.neighbors(i)
        count_A = 0
        count_B = 0
  
        for j in neigh:
            if (G.nodes[j]['action'] == 'A'):
                count_A += 1
            else:
                count_B += 1
        payoff_A = a * count_A
        payoff_B = b * count_B
  
        if (payoff_A >= payoff_B):
            dict1[i] = 'A'
        else:
            dict1[i] = 'B'
    return dict1
  
def reset_node_attributes(G, action_dict):
    for i in action_dict:
        G.nodes[i]['action'] = action_dict[i]
    return G
  
def Calculate(G):
    terminate = True
    count = 0
    c = 0
      
    while (terminate and count < 10):
        count += 1
          
        # action_dict will hold a dictionary
        action_dict = recalculate(G)
        G = reset_node_attributes(G, action_dict)
        colors = get_colors(G)
  
        if (colors.count('red') == len(colors) or colors.count('green') == len(colors)):
            terminate = False
            if (colors.count('green') == len(colors)):
                c = 1
        nx.draw(G, with_labels=1, node_color=colors, node_size=800)
        plt.show()
    if (c == 1):
        print('cascade complete')
    else:
        print('cascade incomplete')
  
  
G = nx.erdos_renyi_graph(10, 0.5)
nx.write_gml(G, "erdos_graph.gml")
  
G = nx.read_gml('erdos_graph.gml')
print(G.nodes())
  
G = set_all_B(G)
  
# initial adopters
list1 = ['2', '1', '3']
G = set_A(G, list1)
colors = get_colors(G)
  
nx.draw(G, with_labels=1, node_color=colors, node_size=800)
plt.show()
  
Calculate(G)

Producción:

['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
cascade complete

2. Personas clave.

# cascade key people
import networkx as nx
import matplotlib.pyplot as plt
  
G = nx.erdos_renyi_graph(10, 0.5)
nx.write_gml(G, "erdos_graph.gml")
  
def set_all_B(G):
    for i in G.nodes():
        G.nodes[i]['action'] = 'B'
    return G
  
def set_A(G, list1):
    for i in list1:
        G.nodes[i]['action'] = 'A'
    return G
  
def get_colors(G):
    color = []
    for i in G.nodes():
        if (G.nodes[i]['action'] == 'B'):
            color.append('red')
        else:
            color.append('green')
    return color
  
  
def recalculate(G):
    dict1 = {}
      
    # payoff(A)=a=4
    # payoff(B)=b=3
    a = 10
    b = 5
    for i in G.nodes():
        neigh = G.neighbors(i)
        count_A = 0
        count_B = 0
  
        for j in neigh:
            if (G.nodes[j]['action'] == 'A'):
                count_A += 1
            else:
                count_B += 1
  
        payoff_A = a * count_A
        payoff_B = b * count_B
  
        if (payoff_A >= payoff_B):
            dict1[i] = 'A'
        else:
            dict1[i] = 'B'
  
    return dict1
  
  
def reset_node_attributes(G, action_dict):
      
    for i in action_dict:
        G.nodes[i]['action'] = action_dict[i]
    return G
  
  
def Calculate(G):
    continuee = True
    count = 0
    c = 0
  
    while (continuee and count < 100):
        count += 1
          
        # action_dict will hold a dictionary
        action_dict = recalculate(G)
        G = reset_node_attributes(G, action_dict)
        colors = get_colors(G)
          
        if (colors.count('red') == len(colors) or colors.count('green') == len(colors)):
            continuee = False
            if (colors.count('green') == len(colors)):
                c = 1
  
    if (c == 1):
        print('cascade complete')
    else:
        print('cascade incomplete')
  
  
G = nx.read_gml('erdos_graph.gml')
  
for i in G.nodes():
    for j in G.nodes():
        if (i < j):
            list1 = []
            list1.append(i)
            list1.append(j)
            print(list1, ':', end="")
  
            G = set_all_B(G)
            G = set_A(G, list1)
            colors = get_colors(G)
            Calculate(G)

Producción:

['0', '1'] :cascade complete
['0', '2'] :cascade incomplete
['0', '3'] :cascade complete
['0', '4'] :cascade complete
['0', '5'] :cascade incomplete
['0', '6'] :cascade complete
['0', '7'] :cascade complete
['0', '8'] :cascade complete
['0', '9'] :cascade complete
['1', '2'] :cascade complete
['1', '3'] :cascade complete
['1', '4'] :cascade complete
['1', '5'] :cascade complete
['1', '6'] :cascade complete
['1', '7'] :cascade complete
['1', '8'] :cascade complete
['1', '9'] :cascade complete
['2', '3'] :cascade incomplete
['2', '4'] :cascade incomplete
['2', '5'] :cascade incomplete
['2', '6'] :cascade incomplete
['2', '7'] :cascade incomplete
['2', '8'] :cascade incomplete
['2', '9'] :cascade complete
['3', '4'] :cascade complete
['3', '5'] :cascade incomplete
['3', '6'] :cascade complete
['3', '7'] :cascade complete
['3', '8'] :cascade complete
['3', '9'] :cascade complete
['4', '5'] :cascade incomplete
['4', '6'] :cascade complete
['4', '7'] :cascade complete
['4', '8'] :cascade complete
['4', '9'] :cascade incomplete
['5', '6'] :cascade incomplete
['5', '7'] :cascade incomplete
['5', '8'] :cascade incomplete
['5', '9'] :cascade complete
['6', '7'] :cascade complete
['6', '8'] :cascade complete
['6', '9'] :cascade complete
['7', '8'] :cascade complete
['7', '9'] :cascade complete
['8', '9'] :cascade complete

3. Impacto de las comunidades en las Cascadas.

import networkx as nx
import random
import matplotlib.pyplot as plt
  
  
def first_community(G):
    for i in range(1, 11):
        G.add_node(i)
    for i in range(1, 11):
        for j in range(1, 11):
            if (i < j):
                r = random.random()
                if (r < 0.5):
                    G.add_edge(i, j)
    return G
  
def second_community(G):
    for i in range(11, 21):
        G.add_node(i)
    for i in range(11, 21):
        for j in range(11, 21):
            if (i < j):
                r = random.random()
                if (r < 0.5):
                    G.add_edge(i, j)
    return G
  
  
G = nx.Graph()
G = first_community(G)
G = second_community(G)
G.add_edge(5, 15)
  
nx.draw(G, with_labels=1)
plt.show()
  
nx.write_gml(G, "community.gml")

Producción:

Impacto en los clústeres

4. Cascada en clústeres.

import networkx as nx
import matplotlib.pyplot as plt
  
  
def set_all_B(G):
    for i in G.nodes():
        G.nodes[i]['action'] = 'B'
    return G
  
def set_A(G, list1):
    for i in list1:
        G.nodes[i]['action'] = 'A'
    return G
  
def get_colors(G):
    color = []
    for i in G.nodes():
        if (G.nodes[i]['action'] == 'B'):
            color.append('red')
        else:
            color.append('green')
    return color
  
def recalculate(G):
    dict1 = {}
    a = 3
    b = 2
    for i in G.nodes():
        neigh = G.neighbors(i)
        count_A = 0
        count_B = 0
  
        for j in neigh:
            if (G.nodes[j]['action'] == 'A'):
                count_A += 1
            else:
                count_B += 1
        payoff_A = a * count_A
        payoff_B = b * count_B
  
        if (payoff_A >= payoff_B):
            dict1[i] = 'A'
        else:
            dict1[i] = 'B'
    return dict1
  
def reset_node_attributes(G, action_dict):
    for i in action_dict:
        G.nodes[i]['action'] = action_dict[i]
    return G
  
def Calculate(G):
    terminate = True
    count = 0
    c = 0
    while (terminate and count < 100):
        count += 1
          
        # action_dict will hold a dictionary
        action_dict = recalculate(G)
        G = reset_node_attributes(G, action_dict)
        colors = get_colors(G)
  
        if (colors.count('red') == len(colors) or colors.count('green') == len(colors)):
            terminate = False
            if (colors.count('green') == len(colors)):
                c = 1
  
    if (c == 1):
        print('cascade complete')
    else:
        print('cascade incomplete')
    nx.draw(G, with_labels=1, node_color=colors, node_size=800)
    plt.show()
  
  
G = nx.Graph()
G.add_nodes_from(range(13))
G.add_edges_from(
    [(0, 1), (0, 6), (1, 2), (1, 8), (1, 12),
     (2, 9), (2, 12), (3, 4), (3, 9), (3, 12),
     (4, 5), (4, 12), (5, 6), (5, 10), (6, 8), 
     (7, 8), (7, 9), (7, 10), (7, 11), (8, 9), 
     (8, 10), (8, 11), (9, 10), (9, 11), (10, 11)])
  
list2 = [[0, 1, 2, 3], [0, 2, 3, 4], [1, 2, 3, 4],
         [2, 3, 4, 5], [3, 4, 5, 6], [4, 5, 6, 12],
         [2, 3, 4, 12], [0, 1, 2, 3, 4, 5], 
         [0, 1, 2, 3, 4, 5, 6, 12]]
  
for list1 in list2:
    print(list1)
    G = set_all_B(G)
  
    G = set_A(G, list1)
    colors = get_colors(G)
    nx.draw(G, with_labels=1, node_color=colors, node_size=800)
    plt.show()
  
    Calculate(G)

Producción:

[0, 1, 2, 3]
cascade incomplete
[0, 2, 3, 4]
cascade incomplete
[1, 2, 3, 4]
cascade incomplete
[2, 3, 4, 5]
cascade incomplete
[3, 4, 5, 6]
cascade incomplete
[4, 5, 6, 12]
cascade incomplete
[2, 3, 4, 12]
cascade incomplete
[0, 1, 2, 3, 4, 5]
cascade incomplete
[0, 1, 2, 3, 4, 5, 6, 12]
cascade complete