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diff --git a/doc/knn.1 b/doc/knn.1 new file mode 100644 index 0000000..b3a63db --- /dev/null +++ b/doc/knn.1 @@ -0,0 +1,158 @@ +.\" generated with Ronn/v0.7.3 +.\" http://github.com/rtomayko/ronn/tree/0.7.3 +. +.TH "KNN" "1" "September 2017" "www.complex-networks.net" "www.complex-networks.net" +. +.SH "NAME" +\fBknn\fR \- Compute the average nearest neighbours degree function +. +.SH "SYNOPSIS" +\fBknn\fR \fIgraph_in\fR [\fINO|LIN|EXP\fR \fIbin_param\fR] +. +.SH "DESCRIPTION" +\fBknn\fR computes the average nearest neighbours degree function knn(k) of the graph \fIgraph_in\fR 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)\. +. +.SH "PARAMETERS" +. +.TP +\fIgraph_in\fR +undirected input graph (edge list)\. If is equal to \fB\-\fR (dash), read the edge list from STDIN\. +. +.TP +NO +If the second (optional) parameter is equal to \fBNO\fR, or omitted, the program will print on output the values of knn(k) for all the degrees in \fIgraph_in\fR\. +. +.TP +LIN +If the second (optional) parameter is equal to \fBLIN\fR, the program will average the values of knn(k) over \fIbin_param\fR bins of equal length\. +. +.TP +EXP +If the second (optional) parameter is equal to \fBEXP\fR, 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, \fIbin_param\fR is the exponent of the increase\. +. +.TP +\fIbin_param\fR +If the second parameter is equal to \fBLIN\fR, \fIbin_param\fR is the number of bins used in the linear binning\. If the second parameter is \fBEXP\fR, \fIbin_param\fR is the exponent used to determine the width of each bin\. +. +.SH "OUTPUT" +The output is in the form: +. +.IP "" 4 +. +.nf + + k1 knn(k1) + k2 knn(k2) + \.\.\.\. +. +.fi +. +.IP "" 0 +. +.P +If no binning is selected, \fBk1\fR, \fBk2\fR, etc\. are the degrees observed in \fIgraph_in\fR\. If linear or exponential binning is required, then \fBk1\fR, \fBk2\fR, etc\. are the right extremes of the corresponding bin\. +. +.SH "EXAMPLES" +To compute the average neanest\-neighbours degree function for a given graph we just run: +. +.IP "" 4 +. +.nf + + $ 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 + $ +. +.fi +. +.IP "" 0 +. +.P +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 \fBer_1000_5000\.net\fR (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\. +. +.P +We can also ask \fBknn\fR to bin the results over 5 bins of equal width by running: +. +.IP "" 4 +. +.nf + + $ knn er_1000_5000\.net LIN 5 + 6 11\.249206 + 10 11\.037634 + 14 10\.919366 + 18 10\.68685 + 22 11\.474138 + $ +. +.fi +. +.IP "" 0 +. +.P +Let us consider the case of \fBmovie_actors\.net\fR, i\.e\. the actors collaboration network\. Here we ask \fBknn\fR to compute the average nearest\-neighbours degrees using exponential binning: +. +.IP "" 4 +. +.nf + + $ 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 + $ +. +.fi +. +.IP "" 0 +. +.P +Notice that, due to the presence of the second parameter \fBEXP\fR, the program has printed on output knn(k) over bins of exponentially increasing width, using an exponent \fB1\.4\fR\. 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\. +. +.SH "SEE ALSO" +knn_w(1), deg_seq(1) +. +.SH "REFERENCES" +. +.IP "\(bu" 4 +V\. Latora, V\. Nicosia, G\. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 7, Cambridge University Press (2017) +. +.IP "" 0 +. +.SH "AUTHORS" +(c) Vincenzo \'KatolaZ\' Nicosia 2009\-2017 \fB<v\.nicosia@qmul\.ac\.uk>\fR\. |