Building multilayer networks

Functions for buiding multilayer networks and/or its characterising matrices, and other basic functions

GetSampleMultiplex()

Get a sample of a Multiplex

BuildExtendedEdgelistFromSupraAdjacencyMatrix()

Builds extended edgelist from supra-adjacency matrix

BuildLayersTensor()

Build layers tensor

BuildSupraAdjacencyMatrixFromEdgeColoredMatrices()

Build supra-adjacency matrix from edge-colored matrices

BuildSupraAdjacencyMatrixFromExtendedEdgelist()

Build supra-adjacency matrix from edge lists

SupraAdjacencyToBlockTensor()

Return block tensor from supra-adjacency matrix

SupraAdjacencyToNetworkList()

Return a list of igraph objects corresponding to layers

SupraAdjacencyToNodesTensor()

Return nodes tensor from supra-adjacency matrix

buildMultilayerNetworkFromMuxvizFiles()

Return a Multilayer Network from Muxviz files

binarizeMatrix()

Binarize a matrix

Aggregation functions

Obtaining aggregated networks from multilayes.

GetAggregateMatrix()

Get aggregate matrix from nodes tensor

GetAggregateMatrixFromNetworkList()

Get aggregate Matrix from network List

GetAggregateMatrixFromSupraAdjacencyMatrix()

Get aggregate matrix from supra-adjacency matrix

GetAggregateNetworkFromNetworkList()

Get aggregate Network from network List

GetAggregateNetworkFromSupraAdjacencyMatrix()

Get aggregate network from supra-adjacency matrix

Centralities

Multilayer centralities.

GetMultiAuthCentrality()

Calculates Multi-Authority-Centrality

GetMultiClosenessCentrality()

Returns Multi Closeness Centrality

GetMultiDegree()

Return total multi-degree, not accounting for interlinks

GetMultiDegreeSum()

Return the Sum of total multi-degree, include multiple times the interlinks

GetMultiEigenvectorCentrality()

Calculates Multi-Eigenvector-Centrality

GetMultiHubCentrality()

Calculates Multi-Hub-Centrality

GetMultiInDegree()

Return the multi-in-degree, not accounting for interlinks

GetMultiInDegreeSum()

Return the Sum of multi-in-degree, include multiple times the interlinks

GetMultiInStrength()

Return the multi-in-Strength, not accounting for interlinks

GetMultiInStrengthSum()

Return the Sum of multi-in-Strength, include multiple times the interlinks

GetMultiKCoreCentrality()

Calculates Multi-KCore Centrality. Computes centrality in each layer separately and then get the max per node.

GetMultiKatzCentrality()

Calculates Multi-Katz Centrality

GetMultiOutDegree()

Return the multi-out-degree, not accounting for interlinks

GetMultiOutDegreeSum()

Return the Sum of multi-out-degree, include multiple times the interlinks

GetMultiOutStrength()

Return the multi-out-Strength, not accounting for interlinks

GetMultiOutStrengthSum()

Return the Sum of multi-out-Strength, include multiple times the interlinks

GetMultiPageRankCentrality()

Calculates Multi-PageRank-Centrality (based on Multi-RandomWalk-Centrality)

GetMultiPathStatistics()

Return statistics based on multilayer paths

GetMultiRWCentrality()

Returns Multi Random Walk Centrality

GetMultiStrength()

Return total multi-strength

GetMultiStrengthSum()

Return the Sum of total multi-Strength, include multiple times the interlinks

GetMultiplexityCentrality()

Calculates Multiplexity Centrality.

getVersatilityProfile()

Return the Versatility Profile for a given centrality

Mesoscale structures

Describing and anlysis the mescoscale structure of multilayer networks.

GetConnectedComponents()

Return the component assignment for each node

GetGiantConnectedComponent()

Return the largest connected component

GetGiantIntersectionComponent()

Return the largest connected component obtained by intersecting LCC of each layer. Assumption: the network is an edge-colored multigraph

GetGiantIntersectionComponentFromNetworkList()

Return the largest connected component obtained by intersecting LCC of each layer. Assumption: the network is an edge-colored multigraph

GetGiantViableComponent()

Return the largest viable cluster

GetGiantViableComponentFromNetworkList()

Return the largest viable cluster from network list. Assumption: the network is an edge-colored multigraph

GetMultilayerCommunities_Infomap()

Return multilayer communities for interconnected multilayer networks

GetMultiplexCommunities_Infomap()

Return multilayer communities. INFOMAP wrapper

GetMultilayerMotifs()

Return the multilayer motifs. Note that even if inter-links are present, they will be neglected and the network treated as an edge-colored multigraph

GetMultilayerMotifsFromNetworkList()

Calculates the Motifs of a Multilayer from a network list

GetMonoplexTriads()

Return the closed triangles from a monoplex network

GetMultiplexTriads()

Return the closed triangles in single layers, aggregate and multilayer network, but working directly with tensors

GetMultiplexTriadsFromNetworkList()

Return the closed triangles in single layers, aggregate and multilayer network

Global Descriptors

GetGlobalNumberTriangles()

Calculate the global number of triangles

GetAverageGlobalClustering()

Calculate Global Clustering Coefficient

GetAverageGlobalNodeOverlappingMatrix()

Calculates the average global node overlap Matrix

GetAverageGlobalOverlapping()

Gets the average global edge overlap on the multilayer

GetAverageGlobalOverlappingMatrix()

Calculates the average global edge overlap Matrix

Dynamics & Co.

Describing, evaluating, and anlysis dynamics on multilayer networks.

GetLaplacianMatrix()

Network combinatorial Laplacian

GetNormalizedLaplacianMatrix()

Network normalized Laplacian

BuildSupraTransitionMatrixFromSupraAdjacencyMatrix()

Build the supra-transition matrix for a multilayer network

BuildTransitionMatrixFromEdgeColoredMatrices()

Random walk transition matrix for an edge-coloured network. Given the node tensor for the edge-coloured multi-layer network the function builds the supra transition matrix for a discrete time RW.

BuildTransitionMatrixFromSingleLayer()

Returns a Transition Matrix from a single Layer

GetCoverageEvolutionMultilayer()

Get the Coverage Evolution of a Multilayer Network

GetCoverageEvolutionEdgeColored()

Get the Coverage Evolution of an edge-colored network

GetCoverageEvolutionSingleLayer()

Get the Coverage Evolution of a single-layer network

Plotting

Plotting routines (documentation is poor, sorry).

plot_multiplex() plot.multiplex()

Plot a multiplex

plot_multiplex3D() plot.multiplex3D()

3D plot of a multiplex

multiplot() multiplot.col() multiplot.row()

Multiplot

layoutMultiplex()

layoutMultiplex

plot_multimotif() plot.multimotif()

Plot multilayer motifs Plot a motif from a motifs table returned by GetMultilayerMotifs.

plot_multimodules() plot.multimodules()

Plot modules

Others

Other functions for building a Configuration Model, for evaluating entropy, for solving the eigenvalue problem, for finding shortest paths, etc.

CanonicalVector()

Return the ith canonical vector of a N-dimesnion basis

GetConfigurationModelTypeIFromNetworkList()

Generate random multiplex networks with fixed degree sequences, while destroying intra-layer degree correlations, but not inter-layer ones

GetConfigurationModelTypeIIFromNetworkList()

Generate random multiplex networks with fixed degree sequences, while destroying both intra- and inter-layer degree correlations

BuildDensityMatrixBGS()

Calculate the density matrix from an adjacency matrix

GetEigenvaluesOfDensityMatrix()

Calculate the eigenvalues of a density matrix

GetEigenvaluesOfDensityMatrixFromAdjacencyMatrix()

Calculate the eigenvalues of a density matrix from an adjacency matrix

GetInterAssortativityTensor()

Return Assortativity Inter-layer values

GetJensenShannonDivergence()

Calculate the Jensen-Shannon Divergence of two networks

GetLargestEigenv()

Gets the largest Eigenvalue from a Matrix. A warning is raised if complex numbers emerge.

GetLocalClustering()

Calculate Local Clustering Coefficient

GetMultilayerReducibility()

Calculate the Reducibility of a multilayer network

GetRenyiEntropyFromAdjacencyMatrix()

Calculate the quantum Renyi entropy of a network

GetRewiredLayerWithOverlappingEdges()

Generate multiplex networks with given amount of edge overlapping

GetSPSimilarityMatrix()

Returns pairwise similarity based on Frobenius norm

MultiShortestPathFromNode()

Return the Shortest-Path from given node to other nodes, with option for counting replicates

ShortestPathFromNode()

Return the Shortest-Path from the given node to other nodes

SolveEigenvalueProblem()

Return the matrix of eigenvectors (Q) and the diagonal matrix of eigenvalues (L) as well as a vector with ordered eigenvalues (E)

Auxiliary functions

MATLAB-like functions that help building multilayers from diagonal, blockdiagonal… matrices.

blkdiag()

Return a list of matrices in block diagonal form

reshapeR()

Return a matrix reshaped according to dimension n and m

diagR()

Return a matrix with elements on a diagonal specified by offset

traceR()

Return the trace of input matrix

modR()

Return the remainder of x divided by y

sumR()

Return the sum across rows (n=1) or columns (n=2) of a matrix

binarizeMatrix()

Binarize a matrix