page_title: Degree-preserving randomization
section_title: Example
hierarchical_section_title: Degree-preserving randomization / Example
caption_attribution_description: English: Blue dots are results of network metrics from individual trials of degree preserving randomization, and the red dot is the observed characteristic for the real network.
context_page_description: Degree Preserving Randomization is a technique used in Network Science that aims to assess whether or not variations observed in a given graph could simply be an artifact of the graph's inherent structural properties rather than properties unique to the nodes, in an observed network.
context_section_description: What follows is a small example showing how one may apply Degree Preserving Randomization to an observed network in an effort to understand the network against otherwise random variation while maintaining the degree distributional aspect of the network. The Association of Internet Researchers has a Listserv that constitutes the majority of discussion threads surrounding their work. On it, members post updates about their own research, upcoming conferences, calls for papers and also engage one another in substantive discussions in their field. These emails can in turn constitute a directed and temporal network graph, where nodes are individual e-mail accounts belonging to the Listserv and edges are cases in which one e-mail address responds to another e-mail address on the Listserv.
  In this observed network, the properties of the Listserv are relatively simple to calculate - for the network of 3,235 individual e-mail accounts and 9,824 exchanges in total, the observed reciprocity of the network is about 0.074, and the [Average path length|average path length] is about 4.46. Could these values be arrived at simply through the nature of the network's inherent structure?
  Applying the  rule, this network would require around 67,861 individual edge rewires to construct a likely sufficiently random degree-preserved graph. If we construct many random, degree preserving graphs from the real graph, we can then create a probability space for characteristics, such as reciprocity and average path length, and assess the degree to which the network could have expressed these characteristics at random. 534 networks were generated using Degree Preserving Randomization. As both reciprocity and average path length in this graph are normally distributed, and as the standard deviation for both reciprocity and average path length are far too narrow to include the observed case, we can reasonably posit that this network is expressing characteristics that are non-random (and thus open for further theory and modeling).
caption: Results from Degree Preserving Randomization Trials.
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