You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
158 lines
7.0 KiB
158 lines
7.0 KiB
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
|
"http://www.w3.org/TR/html4/loose.dtd">
|
|
<html >
|
|
<head><title>2.2.1.0 nibilab_linear_delay</title>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
|
<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
|
|
<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
|
|
<!-- html,index=2,3,4,5,next -->
|
|
<meta name="src" content="mammult_doc.tex">
|
|
<meta name="date" content="2015-10-19 17:14:00">
|
|
<link rel="stylesheet" type="text/css" href="mammult_doc.css">
|
|
</head><body
|
|
>
|
|
<!--l. 5--><div class="crosslinks"><p class="noindent">[<a
|
|
href="mammult_docsu44.html" >next</a>] [<a
|
|
href="mammult_docsu42.html" >prev</a>] [<a
|
|
href="mammult_docsu42.html#tailmammult_docsu42.html" >prev-tail</a>] [<a
|
|
href="#tailmammult_docsu43.html">tail</a>] [<a
|
|
href="mammult_docsu41.html#mammult_docsu43.html" >up</a>] </p></div>
|
|
<h5 class="subsubsectionHead"><a
|
|
id="x51-500002.2.1"></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 –
|
|
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"><</span><span
|
|
class="cmitt-10x-x-109">N</span><span
|
|
class="cmmi-10x-x-109">> <</span><span
|
|
class="cmitt-10x-x-109">m</span><span
|
|
class="cmmi-10x-x-109">> <</span><span
|
|
class="cmitt-10x-x-109">m0</span><span
|
|
class="cmmi-10x-x-109">> <</span><span
|
|
class="cmitt-10x-x-109">outfile</span><span
|
|
class="cmmi-10x-x-109">> <</span><span
|
|
class="cmitt-10x-x-109">a</span><span
|
|
class="cmmi-10x-x-109">> <</span><span
|
|
class="cmitt-10x-x-109">b</span><span
|
|
class="cmmi-10x-x-109">> <</span><span
|
|
class="cmitt-10x-x-109">c</span><span
|
|
class="cmmi-10x-x-109">></span>
|
|
<span
|
|
class="cmmi-10x-x-109"><</span><span
|
|
class="cmitt-10x-x-109">d</span><span
|
|
class="cmmi-10x-x-109">> <</span><span
|
|
class="cmitt-10x-x-109">beta</span><span
|
|
class="cmmi-10x-x-109">></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]
|
|
Π i→j ∝ 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]
|
|
Π i→j ∝ 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">τ </span>sampled from the power-law function:
|
|
<table
|
|
class="equation-star"><tr><td>
|
|
<center class="math-display" >
|
|
<img
|
|
src="mammult_doc17x.png" alt="P(τ) ∼ τ−β
|
|
" 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" >   <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, “Growing multiplex
|
|
networks”, <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>
|
|
|
|
|
|
|
|
<!--l. 5--><div class="crosslinks"><p class="noindent">[<a
|
|
href="mammult_docsu44.html" >next</a>] [<a
|
|
href="mammult_docsu42.html" >prev</a>] [<a
|
|
href="mammult_docsu42.html#tailmammult_docsu42.html" >prev-tail</a>] [<a
|
|
href="mammult_docsu43.html" >front</a>] [<a
|
|
href="mammult_docsu41.html#mammult_docsu43.html" >up</a>] </p></div>
|
|
<!--l. 5--><p class="indent" > <a
|
|
id="tailmammult_docsu43.html"></a>
|
|
</body></html>
|
|
|