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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<div id="projectbrief">A library focused on algorithms on linear arrangements of graphs.</div>
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<li class="navelem"><a class="el" href="dir_8f631ac29b6730c95cdd9d587311e2d3.html">lal</a></li><li class="navelem"><a class="el" href="dir_cc0cd4d6d384fc7709f97ff1416f278a.html">properties</a></li> </ul>
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<div class="headertitle"><div class="title">degrees.hpp</div></div>
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<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">/*********************************************************************</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment"> *</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> * Linear Arrangement Library - A library that implements a collection</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> * algorithms for linear arrangments of graphs.</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"> *</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> * Copyright (C) 2019 - 2021</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> *</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment"> * This file is part of Linear Arrangement Library. To see the full code</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment"> * visit the webpage:</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment"> * https://github.com/lluisalemanypuig/linear-arrangement-library.git</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment"> *</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment"> * Linear Arrangement Library is free software: you can redistribute it</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment"> * and/or modify it under the terms of the GNU Affero General Public License</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment"> * as published by the Free Software Foundation, either version 3 of the</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment"> * License, or (at your option) any later version.</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment"> *</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment"> * Linear Arrangement Library is distributed in the hope that it will be</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment"> * useful, but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment"> * GNU Affero General Public License for more details.</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment"> *</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment"> * You should have received a copy of the GNU Affero General Public License</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment"> * along with Linear Arrangement Library. If not, see <http://www.gnu.org/licenses/>.</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment"> *</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment"> * Contact:</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment"> *</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment"> * Lluís Alemany Puig (lalemany@cs.upc.edu)</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment"> * LARCA (Laboratory for Relational Algorithmics, Complexity and Learning)</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment"> * CQL (Complexity and Quantitative Linguistics Lab)</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment"> * Jordi Girona St 1-3, Campus Nord UPC, 08034 Barcelona. CATALONIA, SPAIN</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment"> * Webpage: https://cqllab.upc.edu/people/lalemany/</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment"> *</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment"> * Ramon Ferrer i Cancho (rferrericancho@cs.upc.edu)</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment"> * LARCA (Laboratory for Relational Algorithmics, Complexity and Learning)</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment"> * CQL (Complexity and Quantitative Linguistics Lab)</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment"> * Office S124, Omega building</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment"> * Jordi Girona St 1-3, Campus Nord UPC, 08034 Barcelona. CATALONIA, SPAIN</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment"> * Webpage: https://cqllab.upc.edu/people/rferrericancho/</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment"> *</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment"> ********************************************************************/</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="preprocessor">#pragma once</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// C++ includes</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// lal includes</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="preprocessor">#include <lal/numeric/rational.hpp></span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="preprocessor">#include <lal/graphs/undirected_graph.hpp></span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="preprocessor">#include <lal/graphs/directed_graph.hpp></span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="preprocessor">#include <lal/graphs/free_tree.hpp></span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="preprocessor">#include <lal/graphs/rooted_tree.hpp></span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespacelal.html">lal</a> {</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="keyword">namespace </span>properties {</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span>numeric::rational</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#a8189ffb3e3386ee95dcf7530011dda01"> 72</a></span><a class="code hl_function" href="namespacelal_1_1properties.html#a8189ffb3e3386ee95dcf7530011dda01">moment_degree_rational</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1undirected__graph.html">graphs::undirected_graph</a>& g, uint32_t p) <span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#afb06b2d8f62bf9603ef2f5adee87d56b"> 82</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespacelal_1_1properties.html#afb06b2d8f62bf9603ef2f5adee87d56b">moment_degree</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1undirected__graph.html">graphs::undirected_graph</a>& g, uint32_t p) <span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><a class="code hl_class" href="classlal_1_1numeric_1_1rational.html">numeric::rational</a></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#a4f4554ea43c1374e040d60cd9a53ac84"> 100</a></span><a class="code hl_function" href="namespacelal_1_1properties.html#a8189ffb3e3386ee95dcf7530011dda01">moment_degree_rational</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1directed__graph.html">graphs::directed_graph</a>& g, uint32_t p) <span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#aa92325006267f83f5f683e9f674942db"> 110</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespacelal_1_1properties.html#afb06b2d8f62bf9603ef2f5adee87d56b">moment_degree</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1directed__graph.html">graphs::directed_graph</a>& g, uint32_t p) <span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> </div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span><a class="code hl_class" href="classlal_1_1numeric_1_1rational.html">numeric::rational</a></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#a9dd093274eff2c3755cd54ae5907a04f"> 127</a></span><a class="code hl_function" href="namespacelal_1_1properties.html#a9dd093274eff2c3755cd54ae5907a04f">moment_degree_in_rational</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1directed__graph.html">graphs::directed_graph</a>& g, uint32_t p) <span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#a5d46daa5e371aa95448f8f31a642bede"> 137</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespacelal_1_1properties.html#a5d46daa5e371aa95448f8f31a642bede">moment_degree_in</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1directed__graph.html">graphs::directed_graph</a>& g, uint32_t p) <span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> </div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span><a class="code hl_class" href="classlal_1_1numeric_1_1rational.html">numeric::rational</a></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#a5efdbc1f5586bca3cdb9b6279051c12b"> 154</a></span><a class="code hl_function" href="namespacelal_1_1properties.html#a5efdbc1f5586bca3cdb9b6279051c12b">moment_degree_out_rational</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1directed__graph.html">graphs::directed_graph</a>& g, uint32_t p) <span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#a14c1ae06978c36d1da71b62bae32304f"> 165</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespacelal_1_1properties.html#a14c1ae06978c36d1da71b62bae32304f">moment_degree_out</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1directed__graph.html">graphs::directed_graph</a>& g, uint32_t p)<span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> </div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#a23f61ed2204c24dce8049666357b65d5"> 186</a></span><a class="code hl_class" href="classlal_1_1numeric_1_1rational.html">numeric::rational</a> <a class="code hl_function" href="namespacelal_1_1properties.html#a23f61ed2204c24dce8049666357b65d5">hubiness_rational</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1free__tree.html">graphs::free_tree</a>& t) <span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> </div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#a1750ada3673e7deba32658dc3da2cf0c"> 207</a></span><a class="code hl_class" href="classlal_1_1numeric_1_1rational.html">numeric::rational</a> <a class="code hl_function" href="namespacelal_1_1properties.html#a23f61ed2204c24dce8049666357b65d5">hubiness_rational</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1rooted__tree.html">graphs::rooted_tree</a>& t) <span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> </div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#ab052d596b426bfa68ca44f046e44e76d"> 218</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespacelal_1_1properties.html#ab052d596b426bfa68ca44f046e44e76d">hubiness</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1free__tree.html">graphs::free_tree</a>& t) <span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> </div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"><a class="line" href="namespacelal_1_1properties.html#af13cc3093569223cde0ae3f329f86ded"> 230</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespacelal_1_1properties.html#ab052d596b426bfa68ca44f046e44e76d">hubiness</a>(<span class="keyword">const</span> <a class="code hl_class" href="classlal_1_1graphs_1_1rooted__tree.html">graphs::rooted_tree</a>& t) <span class="keyword">noexcept</span>;</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span>} <span class="comment">// -- namespace properties</span></div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span>} <span class="comment">// -- namespace lal</span></div>
<div class="ttc" id="aclasslal_1_1graphs_1_1directed__graph_html"><div class="ttname"><a href="classlal_1_1graphs_1_1directed__graph.html">lal::graphs::directed_graph</a></div><div class="ttdoc">Directed graph class.</div><div class="ttdef"><b>Definition</b> directed_graph.hpp:68</div></div>
<div class="ttc" id="aclasslal_1_1graphs_1_1free__tree_html"><div class="ttname"><a href="classlal_1_1graphs_1_1free__tree.html">lal::graphs::free_tree</a></div><div class="ttdoc">Free tree graph class.</div><div class="ttdef"><b>Definition</b> free_tree.hpp:59</div></div>
<div class="ttc" id="aclasslal_1_1graphs_1_1rooted__tree_html"><div class="ttname"><a href="classlal_1_1graphs_1_1rooted__tree.html">lal::graphs::rooted_tree</a></div><div class="ttdoc">Rooted tree graph class.</div><div class="ttdef"><b>Definition</b> rooted_tree.hpp:107</div></div>
<div class="ttc" id="aclasslal_1_1graphs_1_1undirected__graph_html"><div class="ttname"><a href="classlal_1_1graphs_1_1undirected__graph.html">lal::graphs::undirected_graph</a></div><div class="ttdoc">Undirected graph class.</div><div class="ttdef"><b>Definition</b> undirected_graph.hpp:67</div></div>
<div class="ttc" id="aclasslal_1_1numeric_1_1rational_html"><div class="ttname"><a href="classlal_1_1numeric_1_1rational.html">lal::numeric::rational</a></div><div class="ttdoc">Exact rational number.</div><div class="ttdef"><b>Definition</b> rational.hpp:63</div></div>
<div class="ttc" id="anamespacelal_1_1properties_html_a14c1ae06978c36d1da71b62bae32304f"><div class="ttname"><a href="namespacelal_1_1properties.html#a14c1ae06978c36d1da71b62bae32304f">lal::properties::moment_degree_out</a></div><div class="ttdeci">double moment_degree_out(const graphs::directed_graph &g, uint32_t p) noexcept</div><div class="ttdoc">Computes the -th moment of out-degree about zero of a directed graph as a floating point value.</div></div>
<div class="ttc" id="anamespacelal_1_1properties_html_a23f61ed2204c24dce8049666357b65d5"><div class="ttname"><a href="namespacelal_1_1properties.html#a23f61ed2204c24dce8049666357b65d5">lal::properties::hubiness_rational</a></div><div class="ttdeci">numeric::rational hubiness_rational(const graphs::free_tree &t) noexcept</div><div class="ttdoc">Computes the hubiness coefficient as an exact rational number.</div></div>
<div class="ttc" id="anamespacelal_1_1properties_html_a5d46daa5e371aa95448f8f31a642bede"><div class="ttname"><a href="namespacelal_1_1properties.html#a5d46daa5e371aa95448f8f31a642bede">lal::properties::moment_degree_in</a></div><div class="ttdeci">double moment_degree_in(const graphs::directed_graph &g, uint32_t p) noexcept</div><div class="ttdoc">Computes the -th moment of in-degree about zero of a directed graph as a floating point value.</div></div>
<div class="ttc" id="anamespacelal_1_1properties_html_a5efdbc1f5586bca3cdb9b6279051c12b"><div class="ttname"><a href="namespacelal_1_1properties.html#a5efdbc1f5586bca3cdb9b6279051c12b">lal::properties::moment_degree_out_rational</a></div><div class="ttdeci">numeric::rational moment_degree_out_rational(const graphs::directed_graph &g, uint32_t p) noexcept</div><div class="ttdoc">Computes the -th moment of out-degree about zero of a directed graph as an exact rational value.</div></div>
<div class="ttc" id="anamespacelal_1_1properties_html_a8189ffb3e3386ee95dcf7530011dda01"><div class="ttname"><a href="namespacelal_1_1properties.html#a8189ffb3e3386ee95dcf7530011dda01">lal::properties::moment_degree_rational</a></div><div class="ttdeci">numeric::rational moment_degree_rational(const graphs::undirected_graph &g, uint32_t p) noexcept</div><div class="ttdoc">Computes the -th moment of degree about zero of a graph as an exact rational value.</div></div>
<div class="ttc" id="anamespacelal_1_1properties_html_a9dd093274eff2c3755cd54ae5907a04f"><div class="ttname"><a href="namespacelal_1_1properties.html#a9dd093274eff2c3755cd54ae5907a04f">lal::properties::moment_degree_in_rational</a></div><div class="ttdeci">numeric::rational moment_degree_in_rational(const graphs::directed_graph &g, uint32_t p) noexcept</div><div class="ttdoc">Computes the -th moment of in-degree about zero of a directed graph as an exact rational value.</div></div>
<div class="ttc" id="anamespacelal_1_1properties_html_ab052d596b426bfa68ca44f046e44e76d"><div class="ttname"><a href="namespacelal_1_1properties.html#ab052d596b426bfa68ca44f046e44e76d">lal::properties::hubiness</a></div><div class="ttdeci">double hubiness(const graphs::free_tree &t) noexcept</div><div class="ttdoc">Computes the hubiness coefficient as a floating point value.</div></div>
<div class="ttc" id="anamespacelal_1_1properties_html_afb06b2d8f62bf9603ef2f5adee87d56b"><div class="ttname"><a href="namespacelal_1_1properties.html#afb06b2d8f62bf9603ef2f5adee87d56b">lal::properties::moment_degree</a></div><div class="ttdeci">double moment_degree(const graphs::undirected_graph &g, uint32_t p) noexcept</div><div class="ttdoc">Computes the -th moment of degree about zero of a directed graph as a floating point value.</div></div>
<div class="ttc" id="anamespacelal_html"><div class="ttname"><a href="namespacelal.html">lal</a></div><div class="ttdoc">Main namespace of the library.</div><div class="ttdef"><b>Definition</b> definitions.hpp:48</div></div>
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