\documentclass[a4paper,11pt]{book}

\usepackage[british]{babel}
\usepackage[latin1]{inputenc}
\usepackage{hyperref}
\usepackage{amsmath, amssymb}

\newcommand{\lay}[1]{^{[#1]}}
\newcommand{\avg}[1]{\langle #1 \rangle}


\newcommand{\myprogram}[3]{\subsubsection{\texttt{#1}}
  \textbf{NAME}
    
  {\textbf{#1} - #2}
    
  \vspace{0.5cm}
  \noindent
  \textbf{SYNOPSYS}
  
  {\textbf{#1} { }\texttt{\textit{#3} } }
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  \vspace{0.5cm}
  \noindent
  \textbf{DESCRIPTION}

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  \vspace{0.5cm}
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\newcommand{\myreference}[1]{
  \vspace{0.5cm}
  \noindent
  \textbf{REFERENCE}

  {#1}
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%%
%% REFERENCES
%%

\newcommand{\refgrowth}{V. Nicosia, G. Bianconi, V. Latora,
  M. Barthelemy, ``Growing multiplex networks'',
  \textit{Phys. Rev. Lett.} {\bf 111}, 058701 (2013).
  
  Link to paper: \url{http://prl.aps.org/abstract/PRL/v111/i5/e058701}
}
\newcommand{\refnonlinear}{V. Nicosia, G. Bianconi, V. Latora,
  M. Barthelemy, ``Non-linear growth and condensation in multiplex
  networks'', \textit{Phys. Rev. E} {\bf 90}, 042807 (2014).
  
  Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807}
}
\newcommand{\refmetrics}{F. Battiston, V. Nicosia, V. Latora,
  ``Structural measures for multiplex networks'',
  \textit{Phys. Rev. E} {\bf 89}, 032804 (2014).
  
  Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804}
}
\newcommand{\refcorrelations}{V. Nicosia, V. Latora, ``Measuring and
  modeling correlations in multiplex networks'', \textit{Phys. Rev. E}
  {\bf 92}, 032805 (2015).
  
  Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805}}

\newcommand{\refreducibility}{M. De Domenico, V. Nicosia, A. Arenas,
  V. Latora, \textit{``Structural reducibility of multilayer
    networks''}, Nat. Commun. {\bf 6}, 6864 (2015).
  
  Link to paper: \url{http://www.nature.com/ncomms/2015/150423/ncomms7864/full/ncomms7864.html}
}
\newcommand{\refvisibility}{L. Lacasa, V. Nicosia, V. Latora,
  \textit{``Network structure of multivariate time series''}, accepted
  for publication in Scientific Reports, arxiv:1408.0925 (2015).
  
  Link to paper: \url{http://arxiv.org/abs/1408.0925}
}

\newcommand{\refbiased}{F. Battiston, V. Nicosia, V. Latora,
  \textit{``Biased random walks on multiplex networks''}, arxiv:1505.01378 (2015).
  
  Link to paper: \url{http://arxiv.org/abs/1505.01378}
}
\newcommand{\refising}{F. Battiston, A. Cairoli, V. Nicosia, A. Baule, V. Latora,
  \textit{``Interplay between consensus and coherence in a model of interacting opinions''}, accepted
  for publication in Physica D, arxiv:1506.04544 (2015).
  
  Link to paper: \url{http://arxiv.org/abs/1506.04544}
}
\newcommand{\refcommunity}{F. Battiston, J. Iacovacci, V. Nicosia, G. Bianconi, V. Latora,
  \textit{``Emergence of multiplex communities in collaboration networks''}, arxiv:1506.01280 (2015).
  
  Link to paper: \url{http://arxiv.org/abs/1506.01280}
}

\newcommand{\refaxelrod}{F. Battiston, V. Nicosia, V. Latora, M. San Miguel,
  \textit{``Layered social influence promotes multiculturality''}, in preparation (2015).
  
  %Link to paper: \url{http://arxiv.org/abs/inpreparation}
}
\newcommand{\refmotifs}{F. Battiston, M. Chavez, V. Nicosia, V. Latora,
  \textit{``Multilayer motifs in brain networks''}, in preparation (2015).
  
  %Link to paper: \url{http://arxiv.org/abs/inpreparation}
}

\title{MAMMULT: Metrics And Models for MULTilayer networks}


\begin{document}

\maketitle
\tableofcontents

\chapter{Structural descriptors}

\section{Basic node, edge, and layer properties}

\subsection{Node and layer activity}

This section includes programs related to the computation of node and
layer activity, activity vectors, pairwise multiplexity, pairwise
normalised Hamming distance, node degree vectors.

\input{./latex/structure/activity/node_activity.tex}
\input{./latex/structure/activity/layer_activity.tex}
\input{./latex/structure/activity/node_activity_vectors.tex}
\input{./latex/structure/activity/layer_activity_vectors.tex}
\input{./latex/structure/activity/multiplexity.tex}
\input{./latex/structure/activity/hamming_dist.tex}
\input{./latex/structure/activity/node_degree_vectors.tex}
\input{./latex/structure/activity/degs_to_binary.tex}
\input{./latex/structure/activity/degs_to_activity_overlap.tex}

\clearpage

\subsection{Layer aggregation}

This section includes programs to obtain various single-layer
aggregated graphs associated to a multiplex network. 

\input{./latex/structure/metrics/aggregate_layers_w.tex}
\input{./latex/structure/metrics/intersect_layers.tex}
\clearpage

\subsection{Node degree, participation coefficient, cartography}

This section includes programs to compute the total degree and
participation coefficient of each node, and to draw the cartography
diagram of a multiplex.

\input{./latex/structure/metrics/overlap_degree.tex}
\input{./latex/structure/metrics/cartography_from_layers.tex}
\input{./latex/structure/metrics/cartography_from_deg_vectors.tex}
\input{./latex/structure/metrics/cartography_from_columns.tex}
\clearpage

\subsection{Edge overlap, reinforcement}
This section includes programs to compute the egde overlap and to
evaulate the edge reinforcement effect. 

\input{./latex/structure/metrics/edge_overlap.tex}
\input{./latex/structure/metrics/avg_edge_overlap.tex}
\input{./latex/structure/reinforcement/reinforcement.tex}
\clearpage

\section{Inter-layer degree correlations}

\subsection{Node ranking}

This section includes various utilities to compute and compare node
rankings induced by any generic structural node property, including
degree at different layers.

\input{./latex/structure/correlations/rank_nodes.tex}
\input{./latex/structure/correlations/rank_nodes_thresh.tex}
\input{./latex/structure/correlations/rank_occurrence.tex}
\clearpage

\subsection{Interlayer degree correlation coefficients}

This section includes programs for the computation of various
inter-layer degree correlation coefficients.

\input{./latex/structure/correlations/compute_pearson.tex}
\input{./latex/structure/correlations/compute_rho.tex}
\input{./latex/structure/correlations/compute_tau.tex}
\clearpage


\subsection{Interlayer degree correlation functions}

This section includes programs to compute intra-layer and inter-layer
degree correlation functions, and to fit those functions with a
power-law.


\input{./latex/structure/correlations/dump_k_q.tex}
\input{./latex/structure/correlations/knn_q_from_layers.tex}
%% \input{./latex/structure/correlations/knn_q_from_layers_log.tex}
\input{./latex/structure/correlations/knn_q_from_degrees.tex}
%% \input{./latex/structure/correlations/knn_q_from_degrees_log.tex}
\input{./latex/structure/correlations/fit_knn.tex}
\clearpage

\chapter{Models of multi-layer networks}

\section{Null models}

\subsection{Null-models of node and layer activity}

\input{./latex/models/nullmodels/model_hypergeometric.tex}
\input{./latex/models/nullmodels/model_MDM.tex}
\input{./latex/models/nullmodels/model_MSM.tex}
\input{./latex/models/nullmodels/model_layer_growth.tex}
\clearpage


\section{Growing multiplex networks}

\subsection{Linear preferential attachment}

\input{./latex/models/growth/nibilab_linear_delta.tex}
\input{./latex/models/growth/nibilab_linear_delay.tex}
\input{./latex/models/growth/nibilab_linear_delay_mix.tex}
\input{./latex/models/growth/nibilab_linear_random_times.tex}
%%\input{./latex/models/growth/nibilab_semilinear.tex}
\clearpage

\subsection{Non-linear preferential attachment}

\input{./latex/models/growth/nibilab_nonlinear.tex}
\clearpage


\subsection{Utilities}

\input{./latex/models/growth/node_deg_over_time.tex}
\clearpage

\section{Multiplex networks with inter-layer degree correlations}

\subsection{Models based on simulated annealing}

\input{./latex/models/correlations/tune_rho.tex}
\input{./latex/models/correlations/tune_qnn_adaptive.tex}
\clearpage


\chapter{Dynamics on multi-layer networks}

\section{Interacting opinions - Multilayer ising model}

\input{./latex/dynamics/Ising/multiplex_ising.tex}
\clearpage

\section{Biased random walks}

\subsection{Stationary distribution}

\input{./latex/dynamics/randomwalks/statdistr2.tex}
\clearpage

\subsection{Entropy rate}

\input{./latex/dynamics/randomwalks/entropyrate2add.tex}
\input{./latex/dynamics/randomwalks/entropyrate2mult.tex}
\input{./latex/dynamics/randomwalks/entropyrate2int.tex}
\clearpage

\end{document}
