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diff --git a/doc/latex/latex/models/growth/nibilab_nonlinear.tex b/doc/latex/latex/models/growth/nibilab_nonlinear.tex new file mode 100644 index 0000000..2e48a18 --- /dev/null +++ b/doc/latex/latex/models/growth/nibilab_nonlinear.tex @@ -0,0 +1,60 @@ +\myprogram{{nibilab\_nonlinear}} + {Multiplex non-linear preferential attachment model -- + Synchronous arrival.} + {$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$alpha$>$ $<$beta$>$} + +\mydescription{Grow a two-layer multiplex network using the multiplex non-linear + preferential attachment model by Nicosia, Bianconi, Latora, + Barthelemy (NiBiLaB). + + The probability for a newly arrived node $i$ to create a + link to node $j$ on layer $1$ is: + + \begin{equation*} + \Pi_{i\to j}^{1} \propto \frac{\left(k\lay{1}_j\right)^{\alpha}} + {\left(k\lay{2}_j\right)^{\beta}} + \end{equation*} + + and the dual probability for $i$ to create a link to $j$ on + layer $2$ is: + + \begin{equation*} + \Pi_{i\to j}^{2} \propto \frac{\left(k\lay{2}_j\right)^{\alpha}} + {\left(k\lay{1}_j\right)^{\beta}} + \end{equation*} + + Each node arrives simultaneously on both layers. + + + The (mandatory) parameters are as follows: + + \begin{itemize} + + \item \textbf{N} number of nodes in the final graph + + \item \textbf{m} number of new edges brought by each new node + + \item \textbf{m0} number of nodes in the initial seed + graph. \textit{m0} must be larger than of equal + to \textit{m}. + + \item \textbf{outfile} the name of the file which will contain the + + \item \textbf{alpha, beta} exponents of of the attaching probability + function + + \end{itemize} + } + + +\myreturn{The program dumps on the file \texttt{outfile} the + (undirected) edge list of the resulting network. Each line of the + file is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. +} + +\myreference{\refgrowth} |