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.1.html | 239 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 239 insertions(+) create mode 100644 doc/knn.1.html (limited to 'doc/knn.1.html') diff --git a/doc/knn.1.html b/doc/knn.1.html new file mode 100644 index 0000000..c8ea160 --- /dev/null +++ b/doc/knn.1.html @@ -0,0 +1,239 @@ + + + + + + knn(1) - Compute the average nearest neighbours degree function + + + + + +
+ + + +
    +
  1. knn(1)
    2. +
  2. www.complex-networks.net
    3. +
  3. knn(1)
    4. +
+ +

NAME

+

+ knn - 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

+ + + + +

AUTHORS

+ +

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

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