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\myprogram{{nibilab\_linear\_delay}}
{Multiplex linear preferential attachment model --
Asynchronous arrival.}
{$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$a$>$ $<$b$>$
$<$c$>$ $<$d$>$ $<$beta$>$}
\mydescription{Grow a two-layer multiplex network using the multiplex 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 ak\lay{1}_j + bk\lay{2}_j
\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 ck\lay{1}_j + dk\lay{2}_j
\end{equation*}
Each new node arrives first on layer $1$, and its replica on
the layer $2$ appears after a time delay $\tau$ sampled from
the power-law function:
\begin{equation*}
P(\tau) \sim \tau^{-\beta}
\end{equation*}
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{a,b,c,d} the coefficients of the attaching probability
function
\item \textbf{beta} the exponent of the power-law delay
function which determines the arrival of replicas on layer $2$
\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}
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