Abstract
When the network properties of a real-world dataset is computed, we cannot determine from these values per se whether or not the results are surprising or expected. To be able to make these comparisons and judgements, we are in need of a null model whose values can be juxtaposed with the values of a real-world network. This juxtaposition helps us decide which properties are unexpected and require close examination, and which do not. One such null model is the random graph model. This chapter describes in detail the Erdös–Rényi random graph model and the Bollobás configuration random graph model along with some other models that can be used to generate random graphs. The properties of these graphs are also explained.
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References
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Problems
Problems
Download the Astro Physics collaboration network from the SNAP dataset repository available at http://snap.stanford.edu/data/ca-AstroPh.html. This co-authorship network contains 18772 nodes and 198110 edges.
Generate the graph for this dataset (we will refer to this graph as the real world graph).
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Erdös–Rényi random graph (G(n, m): Generate a random instance of this model by using the number of nodes and edges as the real world graph.
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Configuration model random graph: Generate a random instance of this model by using the graph in the dataset.
For each of the real world graph, Erdös–Rényi graph and Cofiguration model graph, compute the following:
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Degree distributions
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Shortest path length distributions
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Clustering coefficient distributions
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WCC size distributions
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For each of these distributions, state whether or not the random models have the same property as the real world graph.
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Are the random graph generators capable of generating graphs that are representative of real world graphs?
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Raj P. M., K., Mohan, A., Srinivasa, K.G. (2018). Random Graph Models. In: Practical Social Network Analysis with Python. Computer Communications and Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-96746-2_3
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DOI: https://doi.org/10.1007/978-3-319-96746-2_3
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