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The probability that the global component q s has

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Unformatted text preview: like) component is composed by the node initially reached, plus k other tree-like components, which have the same size distribution, where k is the number of outgoing links of the node, whose distributionFollowing a random edge is qk . The probability that the global component Q S has size S is thus (A2.6) Q S likely to follow components a size S − of • k times more = qk Prob(union of kedge to has node 1) degree k than a k node of degree 1: (counting the initially reached node in S ). The generating function H1 is by definition qk = kPk / k kPk . H1 (x ) = QS x S, (A2.7) S • There are k − 1 other edges outgoing from this node. k and the distribution of the sum of the sizes of the k components is generated by H1 (as previously explained for the sum of degrees), i.e. • Each one of those k − 1 edges has probability qk of leading to Prob(union of k components has size S ) · x S = ( H1 (x ))k . (A2.8) node of degree k . S A B (Circles denote isolated nodes, squares components of unknown size.) For convenience, define the GF for random edge following (Build up more complex from simpler) ...
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