\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} } } } \newcommand{\mydescription}[1]{ \vspace{0.5cm} \noindent \textbf{DESCRIPTION} {#1} } \newcommand{\myreturn}[1]{ \vspace{0.5cm} \noindent \textbf{OUTPUT} {#1} } \newcommand{\myreference}[1]{ \vspace{0.5cm} \noindent \textbf{REFERENCE} {#1} } %% %% 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}