Read and understand and reproduce a study from an article and implement it in R
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PROJECT 1. Optimality of topological distances.
In subsection "e. Network science"
https://arxiv.org/abs/2007.15342,
we have proposed a new score of the optimality of topological distance in a network, that would be defined as
Omega = (d_r - d)/(d_r - d_min),
where d is the actual mean vertex-vertex distance of a real graph, d_r the mean vertex-vertex distance that is expected in a random model of the original graph and d_min is the minimum mean vertex-vertex distance that a graph preserving certain properties of the original graph (e.g., its number of edges) can achieve. For research on d_min see for instance https://www.nature.com/articles/s42005-019-0239-0.
The main goal of this article is to use Omega to estimate the degree of optimality of topological distances in a collection of real graphs. As a subproblem, a careful choice of d_r and d_min is required (by restricting them to networks with just the same number of edges as the original network).
In subsection "e. Network science"
https://arxiv.org/abs/2007.15342,
we have proposed a new score of the optimality of topological distance in a network, that would be defined as
Omega = (d_r - d)/(d_r - d_min),
where d is the actual mean vertex-vertex distance of a real graph, d_r the mean vertex-vertex distance that is expected in a random model of the original graph and d_min is the minimum mean vertex-vertex distance that a graph preserving certain properties of the original graph (e.g., its number of edges) can achieve. For research on d_min see for instance https://www.nature.com/articles/s42005-019-0239-0.
The main goal of this article is to use Omega to estimate the degree of optimality of topological distances in a collection of real graphs. As a subproblem, a careful choice of d_r and d_min is required (by restricting them to networks with just the same number of edges as the original network).