Related Articles
Cascading Behavior in Social Networks
• Last Updated : 01 Oct, 2020

Prerequisite: Introduction to Social Networks, Python Basics

When people are connected in networks to each other then they can influence each other’s behavior and decisions. This is called Cascading Behavior in Networks.

Let’s consider an example, assume all the people in a society have adopted a trend X. Now there comes new trend Y and a small group accepts this new trend and after this, their neighbors also accept this trend Y and so on.

Example of Cascading Behavior( a=2,b=3 and p=2/5)

So, there are 4 main ideas in Cascading Behaviors:

1. Increasing the payoff.
2. Key people.
3. Impact of communities on the Cascades.
4. Cascading and Clusters.

Below is the code for each idea.

1. Increase the payoff.

## Python3

 # cascade pay offimport networkx as nximport 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 adopterslist1 = ['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)

Output:

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

2. Key people.

## Python3

 # cascade key peopleimport networkx as nximport 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)

Output:

['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. Impact of communities on the Cascades.

## Python3

 import networkx as nximport randomimport 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")

Output:

Impact on clusters

4. Cascading on Clusters.

## Python3

 import networkx as nximport 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)

Output:

[0, 1, 2, 3]
[0, 2, 3, 4]
[1, 2, 3, 4]
[2, 3, 4, 5]
[3, 4, 5, 6]
[4, 5, 6, 12]