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/knn_w.1.html | 222 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 222 insertions(+) create mode 100644 doc/knn_w.1.html (limited to 'doc/knn_w.1.html') diff --git a/doc/knn_w.1.html b/doc/knn_w.1.html new file mode 100644 index 0000000..7f2a11d --- /dev/null +++ b/doc/knn_w.1.html @@ -0,0 +1,222 @@ + + + + + + knn_w(1) - Compute the weighted average nearest neighbours degree function + + + + + +
+ + + +
    +
  1. knn_w(1)
    2. +
  2. www.complex-networks.net
    3. +
  3. knn_w(1)
    4. +
+ +

NAME

+

+ knn_w - Compute the weighted average nearest neighbours degree function +

+ +

SYNOPSIS

+ +

knn_w graph_in [NO|LIN|EXP bin_param]

+ +

DESCRIPTION

+ +

knn_w computes the weighted average nearest neighbours degree +function knn_w(k) of the weighted graph graph_in given as input. The +program can (optionally) average the results over bins of equal or +exponentially increasing width (the latter is also known as +logarithmic binning).

+ +

PARAMETERS

+ +
+
graph_in

undirected and weighted input graph (edge list). If is equal to + - (dash), read the edge list from STDIN.

+
NO

If the second (optional) parameter is equal to NO, or omitted, + the program will print on output the values of knn_w(k) for all the + degrees in graph_in.

+
LIN

If the second (optional) parameter is equal to LIN, the program + will average the values of knn_w(k) over bin_param bins of equal + length.

+
EXP

If the second (optional) parameter is equal to EXP, the progam + will average the values of knn_w(k) over bins of exponentially + increasing width (also known as 'logarithmic binning', which is + odd, since the width of subsequent bins increases exponentially, + not logarithmically, but there you go...). In this case, + bin_param is the exponent of the increase.

+
bin_param

If the second parameter is equal to LIN, bin_param is the + number of bins used in the linear binning. If the second parameter + is EXP, bin_param is the exponent used to determine the width + of each bin.

+
+ + +

OUTPUT

+ +

The output is in the form:

+ +
    k1 knn_w(k1)
+    k2 knn_w(k2)
+    ....
+
+ +

If no binning is selected, k1, k2, etc. are the degrees observed +in graph_in. If linear or exponential binning is required, then +k1, k2, etc. are the right extremes of the corresponding bin.

+ +

EXAMPLES

+ +

To compute the average neanest-neighbours degree function of the US +air transportation network we can run:

+ +
      $ knn_w US_airports.net
+      1 81.8
+      2 30.350938
+      3 15.198846
+      4 15.046341
+      5 13.967998
+      6 16.293341
+      7 11.746223
+      8 11.53912
+      9 7.9134643
+      10 8.317504
+      ....
+      132 0.46248989
+      136 0.47312661
+      145 0.37386548
+      $
+
+ +

Since we have not requested a binning, the program will output the +value of knn_w(k) for each of the degrees actually observed in the +input graph (the mininum degree is 1 and the maximum degree is +145). We can also ask knn_w to bin the results over 10 bins of equal +width by running:

+ +
    $ knn_w US_airports.net 10
+    16 68.359133
+    31 89.519255
+    46 78.911709
+    61 78.802765
+    76 76.352358
+    91 71.589354
+    106 60.433329
+    121 62.600988
+    136 64.81641
+    151 54.210494
+    $
+
+ +

or to use instead an exponential binning:

+ +
    $ knn_w US_airports.net EXP 1.3
+    3 63.062388
+    6 70.319368
+    10 81.856768
+    15 79.766008
+    21 96.172011
+    29 84.771533
+    39 79.591139
+    52 80.222237
+    69 79.776163
+    91 72.217712
+    119 61.878435
+    155 62.695227
+    $
+
+ +

SEE ALSO

+ +

knn(1), deg_seq(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. knn_w(1)
    4. +
+ +
+ + -- cgit v1.2.3