1. knn_w(1)
  2. www.complex-networks.net
  3. knn_w(1)

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

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. October 2020
  3. knn_w(1)