Prerequisites for Random Graph Theory

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I would dearly love to know the prerequisites for self-studying Random Graph Theory and Percolation Theory in Probability.

My knowledge currently involves:

  • Basic probability concepts: the axioms, random variables, distributions.
  • Limit theorems in probability
  • Random Walk

Are these enough or do I need anything extra? It would be great if you kindly pointwise write down ALL the prerequisites, along with a nice book on Random Graphs and Percolation Theory.

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I think the 3 points you listed would satisfy the prerequisites.