Prerequisite: Introduction to Social Networks
K-shell decomposition is the method in which we can divide nodes on the basis of the number of its degree like nodes with degree 1 in one bucket etc.
Consider an example, assume there are n nodes and you apply k-shell decomposition in it. So nodes with degree 1 will be in bucket1 then we will see that after disconnecting these nodes is there any node left with degree 1 if yes then we will add them in bucket 1 and again check and repeat these steps for degree 2, 3, and so on and put them in bucket2, bucket3, etc.
Initial Graph with 7 nodes
In the above graph first, we will put nodes with degree 1 in bucket 1 i.e node 3 and 7. After that, we will remove nodes 3 and 7 and check if there is any node left with degree 1 i.e node 6. Now we will remove node 6 and check any degree 1 node is left which is node 5. So we will remove node 5 and again check but there is no node left with degree 1, so now we will check for nodes with degree 2 which are nodes 1, 2, and 4 and now there is node left in the graph. So bucket1 = [3, 7, 6, 5] and bucket2 = [1, 2, 4].
Below is the implementation of K-shell decomposition on a Social Network:
Python3
# Import required modules import networkx as nx import matplotlib.pyplot as plt # Check if there is any node left with degree d def check(h, d): f = 0 # there is no node of deg <= d for i in h.nodes(): if (h.degree(i) <= d): f = 1 break return f # Find list of nodes with particular degree def find_nodes(h, it): set1 = [] for i in h.nodes(): if (h.degree(i) <= it): set1.append(i) return set1 # Create graph object and add nodes g = nx.Graph() g.add_edges_from( [(1, 2), (1, 9), (3, 13), (4, 6), (5, 6), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (5, 12), (10, 12), (10, 13), (11, 14), (12, 14), (12, 15), (13, 14), (13, 15), (13, 17), (14, 15), (15, 16)]) # Copy the graph h = g.copy() it = 1 # Bucket being filled currently tmp = [] # list of lists of buckets buckets = [] while (1): flag = check(h, it) if (flag == 0): it += 1 buckets.append(tmp) tmp = [] if (flag == 1): node_set = find_nodes(h, it) for each in node_set: h.remove_node(each) tmp.append(each) if (h.number_of_nodes() == 0): buckets.append(tmp) breakprint(buckets) # Illustrate the Social Network # in the form of a graph nx.draw(g, with_labels=1) plt.show() |
Output:
[[2, 3, 4, 7, 8, 17, 16, 1, 6, 9], [11, 5, 10, 13, 12, 14, 15]]
Graph with 17 nodes
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