Random Graph Models for Networks 1.1 Graph Modeling
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چکیده
1.2 Erdős-Renyi Model The above approach constitutes the sampling view of generating a random graph. Alternatively we can take a constructive view where we start with vertex set V = {1, 2, 3....n}, and selecting uniformly at random one edge from those edges not yet chosen, repeating this m times. Definition 3 G(n, p) is the random graph obtained by starting with vertex set V = {1, 2, 3...n}, letting 0 ≤ p ≤ 1, and connecting each pair vertices {i, j} by a edge with probability p This model is typically referred to as the Erdos-Renyi (ER) Random Graph Model, outlined by Erdős and Renyi in two papers from 1959 and 1960 [2, 3]. While the model bears their names, their work initially examined the properties of the G(n,m) model, only later expanding to analyze
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