How to prove if we have ‘p = (1 + e) / n’ for e > 0 in Erdos Renyi model, then we have a ‘unique’ giant component? I am also confused about meaning of giant component! In Wikipedia giant component is a component with n^2/3 nodes.
2026-03-25 07:41:08.1774424468
Giant component in Erdos Renyi model
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Please have a look at theorem 2.14 of the following book https://www.google.co.uk/url?sa=t&source=web&rct=j&url=https://www.math.cmu.edu/~af1p/BOOK.pdf&ved=2ahUKEwjsk9yZo5_bAhWhD8AKHVBcCXIQFjAAegQIBBAB&usg=AOvVaw1IzN2wWofyzT4dxvLwRIhZ.
It shows why the giant component is unique.
Also the giant component has a fraction of all the n vertices of the graph, so it is of linear order on the number of vertices.