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# A21 diagrammatic visualization of a equation a29 and

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Unformatted text preview: i.e. of vulnerable nodes found GF for size of component made S Prob(union by following initial)edge: H1 (x ))k . of k components has size S · x S = ( (A2.8) A B H1(x) = [1 − G1(1)] + xG1(H1(x)). Fig. A2.1. Diagrammatic visualization of (A) Equation (A2.9) and (B) Equation (A2.10). Each square corresponds to an arbitrary tree-like cluster, while the circle is a node of the network. GF for size of component made of vulnerable nodes found by choosing arbitrary node: B Fig. A2.1. Diagrammatic visualization of (A) Equation (A2.9) and (B) Equation (A2.10). Each square corresponds to an arbitrary tree-like cluster, while the circle is a node of H network.[1 − G (1)] + xG (H (x)). the (x) = 0 0 0 1 This leads to the cascade condition: k k (k − 1)ρk Pk > k Results: Theory and simulation Uniform thresholds on random graph where all nodes have degree z (a z -regular random graph) Results: Theory and simulation (a) Normally distributed thresholds with std dev σ , on z -regular random graph. (b) Uniform threshold on regular vs power law random graph. . 3. Cumulative distributions of cascade sizes at the lower a...
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