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.1.html | 190 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 190 insertions(+) create mode 100644 doc/conf_model_deg.1.html (limited to 'doc/conf_model_deg.1.html') diff --git a/doc/conf_model_deg.1.html b/doc/conf_model_deg.1.html new file mode 100644 index 0000000..c70ebdf --- /dev/null +++ b/doc/conf_model_deg.1.html @@ -0,0 +1,190 @@ + + + + + + conf_model_deg(1) - Sample a simple graph from the configuration model + + + + + +
+ + + +
    +
  1. conf_model_deg(1)
    2. +
  2. www.complex-networks.net
    3. +
  3. conf_model_deg(1)
    4. +
+ +

NAME

+

+ conf_model_deg - Sample a simple graph from the configuration model +

+ +

SYNOPSIS

+ +

conf_model_deg degs [threshold]

+ +

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 +degs.

+ +

PARAMETERS

+ +
+
degs

The name of the file containing the degree sequence. If degs is + equal to '-' (dash) the degree sequence is read from STDIN + (standard input).

+
threshold:

+ +

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). 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

+ + + + +

AUTHORS

+ +

(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.

+ + +
    +
  1. www.complex-networks.net
    2. +
  2. September 2017
    3. +
  3. conf_model_deg(1)
    4. +
+ +
+ + -- cgit v1.2.3