Question

Consider an Erdős-Rényi network with N = 3,000 nodes, connected to each other with probability p = 10^–3.

Given the linking probability p = 10^–3, calculate the number of nodes N^cr so that the network has only one component.

Answer 1

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ANSWER::-

AS FOR GIVEN DATA....

Consider an Erdős-Rényi network with N = 3,000 nodes, connected to each other with probability p = 10–3.

Given the linking probability p = 10–3, calculate the number of nodes Ncr so that the network has only one component.

SOL ::-

NOTE ::-

There are two closely related variants of the Erdos–Rényi (ER) random graph model.

In the G(n, M) model, a graph is chosen uniformly at random from the collection of all graphs which have n nodes and M edges. For example, in the G(3, 2) model, each of the three possible graphs on three vertices and two edges are included with probability 1/3.
In the G(n, p) model, a graph is constructed by connecting nodes randomly. Each edge is included in the graph with probability p independent from every other edge. Equivalently, all graphs with n nodes and M edges have equal probability of

CODE ::-

#importing the networkx library >>> import networkx as nx    #importing the matplotlib library for plotting the graph >>> import matplotlib.pyplot as plt    >>> G= nx.erdos_renyi_graph(3000,0.1) >>> nx.draw(G, with_labels=True) >>> plt.show() >>> I= nx.erdos_renyi_graph(3000,0.1) >>> nx.draw(I, with_labels=True) >>> plt.show()

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