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

---
 doc/knn.md | 148 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 148 insertions(+)
 create mode 100644 doc/knn.md

(limited to 'doc/knn.md')

diff --git a/doc/knn.md b/doc/knn.md
new file mode 100644
index 0000000..9646f79
--- /dev/null
+++ b/doc/knn.md
@@ -0,0 +1,148 @@
+knn(1) -- Compute the average nearest neighbours degree function
+======
+
+## SYNOPSIS
+
+`knn` <graph_in> [<NO|LIN|EXP> <bin_param>]
+
+## DESCRIPTION
+
+`knn` computes the average nearest neighbours degree function knn(k)
+of the 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 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(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(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(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(k1)
+        k2 knn(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 for a given
+graph we just run:
+
+          $ knn er_1000_5000.net 
+          2 10.5
+          3 11.333333
+          4 10.785714
+          5 11.255319
+          6 11.336601
+          7 11.176292
+          8 11.067568
+          9 11.093519
+          10 10.898438
+          11 10.906009
+          12 11.031353
+          13 10.73938
+          14 10.961538
+          15 10.730864
+          16 10.669118
+          17 10.702206
+          18 10.527778
+          19 11.302632
+          20 11.8
+          $
+
+Since we have not requested a binning, the program will output the
+value of knn(k) for each of the degrees actually observed in the graph
+`er_1000_5000.net` (the mininum degree is 2 and the maximum degree is
+20). Notice that in this case, as expected in a graph without
+degree-degree correlations, the values of knn(k) are almost
+independent of k. 
+
+We can also ask `knn` to bin the results over 5 bins of equal width by
+running:
+    
+        $ knn er_1000_5000.net LIN 5
+        6 11.249206
+        10 11.037634
+        14 10.919366
+        18 10.68685
+        22 11.474138
+        $
+
+Let us consider the case of `movie_actors.net`, i.e. the actors
+collaboration network. Here we ask `knn` to compute the average
+nearest-neighbours degrees using exponential binning:
+
+        $ knn movie_actors.net EXP 1.4
+        2 142.56552
+        5 129.09559
+        9 158.44493
+        15 198.77922
+        23 205.96538
+        34 210.07379
+        50 227.57167
+        72 235.89857
+        102 254.47583
+        144 276.572
+        202 307.11004
+        283 337.83733
+        397 370.34222
+        556 410.89117
+        779 446.66331
+        1091 498.73118
+        1527 547.31923
+        2137 577.87852
+        2991 582.6855
+        4187 557.44801
+        $
+
+Notice that, due to the presence of the second parameter `EXP`, the
+program has printed on output knn(k) over bins of exponentially
+increasing width, using an exponent `1.4`. This is useful for plotting
+with log or semilog axes. In this case, the clear increasing trend of
+knn(k) indicates the presence of assortative correlations.
+
+## SEE ALSO
+
+knn_w(1), deg_seq(1)
+
+## REFERENCES
+
+* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+  Methods and Applications", Chapter 7, Cambridge University Press
+  (2017)
+
+
+## AUTHORS
+
+(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 `<v.nicosia@qmul.ac.uk>`.
-- 
cgit v1.2.3