From 3aee2fd43e3059a699af2b63c6f2395e5a55e515 Mon Sep 17 00:00:00 2001 From: KatolaZ Date: Wed, 27 Sep 2017 15:06:31 +0100 Subject: First commit on github -- NetBunch 1.0 --- doc/conf_model_deg.md | 97 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 97 insertions(+) create mode 100644 doc/conf_model_deg.md (limited to 'doc/conf_model_deg.md') diff --git a/doc/conf_model_deg.md b/doc/conf_model_deg.md new file mode 100644 index 0000000..9022646 --- /dev/null +++ b/doc/conf_model_deg.md @@ -0,0 +1,97 @@ +conf_model_deg(1) -- Sample a simple graph from the configuration model +====== + +## SYNOPSIS + +`conf_model_deg` [] + +## DESCRIPTION + +`conf_model_deg` samples a simple random undirected graph (i.e., a +graph without self-loops and multiple edges) from the configuration +model associated to the degree sequence provided in the input file +. + +## PARAMETERS + +* : + The name of the file containing the degree sequence. If is + equal to '-' (dash) the degree sequence is read from STDIN + (standard input). + +* : + + Optional number of edge stubs that are allowed to remain + unmatched. This is useful to create graphs from too-constrained + degree sequences (see [EXAMPLES][] below). + + +## OUTPUT + +`conf_model_deg` prints on output the edge list of the sampled graph, +and reports on STDERR whether it has been able to find a graph. + + +## EXAMPLES + +Let us assume that the file `pl_-3.0_3_500_10000` contains a power-law +degree sequence ('gamma=-3.0', 'k_min=3', 'k_max=500', 'N=10000'), for +instance created using [power_law(1)][power_law(1)]. We can sample a +simple configuration model graph having that degree sequence using: + + $ conf_model_deg pl_-3.0_3_500_10000 > conf_model_-3.0_3_500_10000.net + +where we have redirected the output (the resulting edge list) to the +file `conf_model_-3.0_3_500_10000.net`. In this case it is not +necessary to specify a threshold, since the maximum degree in the +sequence is 126, which is smaller than the structural cut-off. + +Let us assume now that the file `AS-20010316.net_degs` contains the +degree sequence of the data set `AS-20010316.net` (the graph of the +Internet at AS level in March 2001). In this case, the degree sequence +is too constrained, since the maximum degree (2277) is much larger +than the structural cut-off (see [REFERENCES][] below). So if we don't +specify a threshold, we get: + + $ conf_model_deg AS-20010316.net_degs > AS_20010316_rand.net + Graph not found (unmatched stubs: 986 > threshold: 0) + Graph not found (unmatched stubs: 888 > threshold: 0) + Graph not found (unmatched stubs: 974 > threshold: 0) + ..... + +and so on, since `conf_model_deg` is trying to match all the edge +stubs, without success. From the messages printed by `conf_model_deg` +on STDERR we notice that the number of unmatched stubs is 986 in the +first attempt, 888 in the second one, and so on, while the acceptable +threshold is set to 0. If we instead specify a reasonable threshold +(in this example set to 950): + + $ conf_model_deg AS-20010316.net_degs 950 > AS_20010316_rand.net + Graph not found (unmatched stubs: 978 > threshold: 950) + Found a graph (unmatched stubs: 876 <= threshold: 950) + $ + +`conf_model_deg` is able to create a graph after a few +attempts. Notice that in the resulting graph 876 of the original edge +stubs will remain unmatched, meaning that the resulting graph has +876/2=438 edges less than those contained in the original graph. + +## SEE ALSO + +deg_seq(1), conf_model_deg_nocheck(1), power_law(1), hv_net(1) + + +## REFERENCES + +* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, + Methods and Applications", Chapter 5, Cambridge University Press + (2017) + +* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, + Methods and Applications", Appendix 12, Cambridge University Press + (2017) + + +## AUTHORS + +(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 ``. -- cgit v1.2.3