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   <h5 class="subsubsectionHead"><a 
 id="x50-490002.2.1"></a><span 
class="cmtt-10x-x-109">nibilab</span><span 
class="cmtt-10x-x-109">_linear</span><span 
class="cmtt-10x-x-109">_delay</span></h5>
<!--l. 5--><p class="noindent" ><span 
class="cmbx-10x-x-109">NAME</span>
<!--l. 5--><p class="indent" >   <span 
class="cmbx-10x-x-109">nibilab</span><span 
class="cmbx-10x-x-109">_linear</span><span 
class="cmbx-10x-x-109">_delay </span>- Multiplex linear preferential attachment model &#8211;
Asynchronous arrival.
<!--l. 5--><p class="noindent" ><span 
class="cmbx-10x-x-109">SYNOPSYS</span>
<!--l. 5--><p class="indent" >   <span 
class="cmbx-10x-x-109">nibilab</span><span 
class="cmbx-10x-x-109">_linear</span><span 
class="cmbx-10x-x-109">_delay  </span><span 
class="cmmi-10x-x-109">&#x003C;</span><span 
class="cmitt-10x-x-109">N</span><span 
class="cmmi-10x-x-109">&#x003E; &#x003C;</span><span 
class="cmitt-10x-x-109">m</span><span 
class="cmmi-10x-x-109">&#x003E; &#x003C;</span><span 
class="cmitt-10x-x-109">m0</span><span 
class="cmmi-10x-x-109">&#x003E; &#x003C;</span><span 
class="cmitt-10x-x-109">outfile</span><span 
class="cmmi-10x-x-109">&#x003E; &#x003C;</span><span 
class="cmitt-10x-x-109">a</span><span 
class="cmmi-10x-x-109">&#x003E; &#x003C;</span><span 
class="cmitt-10x-x-109">b</span><span 
class="cmmi-10x-x-109">&#x003E; &#x003C;</span><span 
class="cmitt-10x-x-109">c</span><span 
class="cmmi-10x-x-109">&#x003E;</span>
<span 
class="cmmi-10x-x-109">&#x003C;</span><span 
class="cmitt-10x-x-109">d</span><span 
class="cmmi-10x-x-109">&#x003E; &#x003C;</span><span 
class="cmitt-10x-x-109">beta</span><span 
class="cmmi-10x-x-109">&#x003E;</span>
<!--l. 54--><p class="noindent" ><span 
class="cmbx-10x-x-109">DESCRIPTION</span>
<!--l. 54--><p class="indent" >   Grow a two-layer multiplex network using the multiplex linear preferential
attachment model by Nicosia, Bianconi, Latora, Barthelemy (NiBiLaB).
<!--l. 54--><p class="indent" >   The probability for a newly arrived node <span 
class="cmmi-10x-x-109">i </span>to create a link to node <span 
class="cmmi-10x-x-109">j </span>on layer
1 is:
   <table 
class="equation-star"><tr><td>
   <center class="math-display" >
<img 
src="mammult_doc15x.png" alt="  1       [1]    [2]
&Pi; i&rarr;j &prop;  akj + bkj
" class="math-display" ></center></td></tr></table>
<!--l. 54--><p class="nopar" >
<!--l. 54--><p class="indent" >   and the dual probability for <span 
class="cmmi-10x-x-109">i </span>to create a link to <span 
class="cmmi-10x-x-109">j </span>on layer 2 is:
   <table 
class="equation-star"><tr><td>
   <center class="math-display" >
<img 
src="mammult_doc16x.png" alt="  2       [1]    [2]
&Pi; i&rarr;j &prop;  ck j + dkj
" class="math-display" ></center></td></tr></table>
<!--l. 54--><p class="nopar" >
<!--l. 54--><p class="indent" >   Each new node arrives first on layer 1, and its replica on the layer 2 appears
after a time delay <span 
class="cmmi-10x-x-109">&tau; </span>sampled from the power-law function:
   <table 
class="equation-star"><tr><td>
   <center class="math-display" >
<img 
src="mammult_doc17x.png" alt="P(&tau;) &sim; &tau;&minus;&beta;
" class="math-display" ></center></td></tr></table>
<!--l. 54--><p class="nopar" >
<!--l. 54--><p class="indent" >   The (mandatory) parameters are as follows:
     <ul class="itemize1">
     <li class="itemize"><span 
class="cmbx-10x-x-109">N </span>number of nodes in the final graph
     </li>
     <li class="itemize"><span 
class="cmbx-10x-x-109">m </span>number of new edges brought by each new node
     </li>
     <li class="itemize"><span 
class="cmbx-10x-x-109">m0 </span>number of nodes in the initial seed graph. <span 
class="cmti-10x-x-109">m0 </span>must be larger than
     of equal to <span 
class="cmti-10x-x-109">m</span>.
     </li>
     <li class="itemize"><span 
class="cmbx-10x-x-109">outfile </span>the name of the file which will contain the
     </li>
     <li class="itemize"><span 
class="cmbx-10x-x-109">a,b,c,d </span>the coefficients of the attaching probability function
     </li>
     <li class="itemize"><span 
class="cmbx-10x-x-109">beta </span>the exponent of the power-law delay function which determines
     the arrival of replicas on layer 2
     </li></ul>
                                                                     

                                                                     
<!--l. 65--><p class="noindent" ><span 
class="cmbx-10x-x-109">OUTPUT</span>
<!--l. 65--><p class="indent" >   The program dumps on the file <span 
class="cmtt-10x-x-109">outfile </span>the (undirected) edge list of the
resulting network. Each line of the file is in the format:
<!--l. 65--><p class="indent" >   &#x00A0;    <span 
class="cmti-10x-x-109">src</span><span 
class="cmti-10x-x-109">_ID dest</span><span 
class="cmti-10x-x-109">_ID</span>
<!--l. 65--><p class="indent" >   where <span 
class="cmti-10x-x-109">src</span><span 
class="cmti-10x-x-109">_ID </span>and <span 
class="cmti-10x-x-109">dest</span><span 
class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
edge.
<!--l. 67--><p class="noindent" ><span 
class="cmbx-10x-x-109">REFERENCE</span>
<!--l. 67--><p class="indent" >   V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, &#8220;Growing multiplex
networks&#8221;, <span 
class="cmti-10x-x-109">Phys. Rev. Lett. </span><span 
class="cmbx-10x-x-109">111</span>, 058701 (2013).
<!--l. 67--><p class="indent" >   Link to paper: <a 
href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span 
class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
                                                                     

                                                                     
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