From 3aee2fd43e3059a699af2b63c6f2395e5a55e515 Mon Sep 17 00:00:00 2001
From: KatolaZ <katolaz@freaknet.org>
Date: Wed, 27 Sep 2017 15:06:31 +0100
Subject: First commit on github -- NetBunch 1.0

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+knn_w(1) -- 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
+
+* A\. Barrat et al. "The architecture of complex weighted
+  networks". P. Natl. Acad. Sci USA 101 (2004), 3747-3752.
+
+* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+  Methods and Applications", Chapter 10, Cambridge University Press
+  (2017)
+
+## AUTHORS
+
+(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 `<v.nicosia@qmul.ac.uk>`.
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