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Consider a large Erdos-Renyi random network- Let S denote the fraction.pdf

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Consider a large Erdos-Renyi random network. Let S denote the fraction of nodes within the largest component. (a) What is the probability that a node with degree k is not in the largest component? (b) Let C denote the set of nodes in the largest component. Let i be a node in the network. Find the probability P ( k i = k i / C ) that a node has degree k given that the node is not part of the largest component. (Hint: Bayes' Theorem may be useful here: P ( A B ) = P ( B A ) P ( A ) / P ( B ) ).

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Consider a large Erdos-Renyi random network. Let S denote the fraction of nodes within the largest component. (a) What is the probability that a node with degree k is not in the largest component? (b) Let C denote the set of nodes in the largest component. Let i be a node in the network. Find the probability P ( k i = k i / C ) that a node has degree k given that the node is not part of the largest component. (Hint: Bayes' Theorem may be useful here: P ( A B ) = P ( B A ) P ( A ) / P ( B ) )

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Consider a large Erdos-Renyi random network- Let S denote the fraction.pdf

  • 1. Consider a large Erdos-Renyi random network. Let S denote the fraction of nodes within the largest component. (a) What is the probability that a node with degree k is not in the largest component? (b) Let C denote the set of nodes in the largest component. Let i be a node in the network. Find the probability P ( k i = k i / C ) that a node has degree k given that the node is not part of the largest component. (Hint: Bayes' Theorem may be useful here: P ( A B ) = P ( B A ) P ( A ) / P ( B ) )