Structure-function multilayer network integration and cognition in multiple sclerosis.
The 2 matches
- [1] § METHODS › Network Construction › Multilayer networks. ↔ multinetx/core/multilayer.py, lines 53–138 · score 0.67 · MultiNetX, adjacency matrices, diagonal, NetworkX, Python, multilayer
- [2] § METHODS › Network Construction › Multilayer networks. ↔ multinetx/__init__.py, lines 27–41 · score 0.53 · NetworkX, multiNetX, Python, multilayer
Paper
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The authors' code
Python · 266 lines · 9.4 KB · no license · 1 match
- #! /usr/bin/env python
- # -*- coding: utf-8 -*-
- ########################################################################
- #
- # multiNetX -- a python package for general multilayer graphs
- #
- # (C) Copyright 2013-2019, Nikos E Kouvaris
- # multiNetX is part of the deliverables of the LASAGNE project
- # (multi-LAyer SpAtiotemporal Generalized NEtworks),
- # EU/FP7-2012-STREP-318132 (http://complex.ffn.ub.es/~lasagne/)
- #
- # multiNetX is free software: you can redistribute it and/or modify
- # it under the terms of the GNU General Public License as published
- # by the Free Software Foundation, either version 3 of the License,
- # or (at your option) any later version.
- #
- # multiNetX is distributed in the hope that it will be useful,
- # but WITHOUT ANY WARRANTY; without even the implied warranty of
- # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
- # See the GNU General Public License for more details.
- #
- # You should have received a copy of the GNU General Public License
- # along with this program. If not, see http://www.gnu.org/licenses/.
- ########################################################################
- """
- MultilayerGraph: Base class for a multi-layer network
- """
- from multinetx.core.exceptions import multinetxError
- # import copy
- try:
- from networkx import Graph, disjoint_union_all
- except ImportError:
- raise ImportError("NetworkX is required")
- try:
- from numpy import zeros
- except ImportError:
- raise ImportError("NumPy is required")
- try:
- from scipy.sparse import lil_matrix
- except ImportError:
- raise ImportError("SciPy is required")
- class MultilayerGraph(Graph):
- """"Define constructor of the class"""
- def __init__(self, list_of_layers=None, inter_adjacency_matrix=None, **attr):
- """Constructor of a MultilayerGraph.
- It creates a symmetric (undirected) MultilayerGraph object
- inheriting methods from networkx.Graph
- Parameters:
- -----------
- list_of_layers : Python list of networkx.Graph objects
- inter_adjacency_matrix : a lil sparse matrix (NxN) with zero
- diagonal elements and off-diagonal
- block elements defined by the
- inter-connectivity architecture.
- Return: a MultilayerGraph object
- Examples:
- ---------
- import multinetx as mx
- import numpy as np
- N = 10
- g1 = mx.erdos_renyi_graph(N,0.07,seed=218)
- g2 = mx.erdos_renyi_graph(N,0.07,seed=211)
- g3 = mx.erdos_renyi_graph(N,0.07,seed=211)
- adj_block = mx.lil_matrix(np.zeros((N*3,N*3)))
- adj_block[0: N, N:2*N] = np.identity(N) # L_12
- adj_block[0: N,2*N:3*N] = np.identity(N) # L_13
- #adj_block[N:2*N,2*N:3*N] = np.identity(N) # L_23
- adj_block += adj_block.T
- mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3],
- inter_adjacency_matrix=adj_block)
- mg.set_edges_weights(inter_layer_edges_weight=4)
- mg.set_intra_edges_weights(layer=0,weight=1)
- mg.set_intra_edges_weights(layer=1,weight=2)
- mg.set_intra_edges_weights(layer=2,weight=3)
- """
- # Give an empty graph in the list_of_layers
- if list_of_layers is None:
- self.list_of_layers = [Graph()]
- self.num_nodes_in_layers = []
- else:
- self.list_of_layers = list_of_layers
- self.num_nodes_in_layers = [
- layer.number_of_nodes() for layer in list_of_layers
- ]
- # Number of nodes
- self.num_nodes = sum(self.num_nodes_in_layers)
- # Create the MultilayerGraph without inter-layer links.
- try:
- Graph.__init__(self, Graph(disjoint_union_all(self.list_of_layers), **attr))
- except multinetxError:
- raise multinetxError("Multiplex cannot inherit Graph properly")
- # Make a zero lil matrix for inter_adjacency_matrix
- if inter_adjacency_matrix is None:
- inter_adjacency_matrix = lil_matrix(zeros((self.num_nodes, self.num_nodes)))
- # Check if the matrix inter_adjacency_matrix is lil
- try:
- assert inter_adjacency_matrix.format == "lil"
- except AssertionError:
- raise multinetxError(
- "interconnecting_adjacency_matrix\
- is not scipy.sparse.lil"
- )
- # Lists for intra-layer and inter-layer edges
- if list_of_layers is None:
- self.intra_layer_edges = []
- else:
- self.intra_layer_edges = self.edges()
- self.inter_layer_edges = []
- # Inter-layer connection
- self.layers_interconnect(inter_adjacency_matrix)
- # MultiNetX name
- self.name = "multilayer"
- for layer in self.list_of_layers:
- self.name += "_" + layer.name
- # Constructor
- # Define methods of the class
- def add_layer(self, layer, **attr):
- if self.num_nodes is 0:
- self.list_of_layers = [layer]
- else:
- self.list_of_layers.append(layer)
- self.num_nodes_in_layers.append(layer.number_of_nodes())
- self.num_nodes = sum(self.num_nodes_in_layers)
- for i, j in layer.edges():
- self.intra_layer_edges.append(
- (
- i + (len(self.list_of_layers) - 1) * layer.number_of_nodes(),
- j + (len(self.list_of_layers) - 1) * layer.number_of_nodes(),
- )
- )
- try:
- Graph.__init__(
- self, Graph(disjoint_union_all(self.list_of_layers), **attr)
- )
- except multinetxError:
- raise multinetxError("Multiplex cannot inherit Graph properly")
- def layers_interconnect(self, inter_adjacency_matrix=None):
- """Parameters:
- -----------
- Examples:
- ---------
- """
- # Make a zero lil matrix for inter_adjacency_matrix
- if inter_adjacency_matrix is None:
- inter_adjacency_matrix = lil_matrix(zeros((self.num_nodes, self.num_nodes)))
- # Check if the matrix inter_adjacency_matrix is lil
- try:
- assert inter_adjacency_matrix.format == "lil"
- except AssertionError:
- raise multinetxError(
- "interconnecting_adjacency_matrix\
- is not scipy.sparse.lil"
- )
- for i, row in enumerate(inter_adjacency_matrix.rows):
- for pos, j in enumerate(row):
- if i > j:
- self.inter_layer_edges.append((i, j))
- self.add_edges_from(self.inter_layer_edges)
- def get_number_of_layers(self):
- """Return the number of graphs"""
- return len(self.list_of_layers)
- def get_number_of_nodes_in_layers(self):
- """Return the number of nodes in each graph"""
- return self.num_nodes_in_layers
- def get_number_of_nodes(self):
- return self.num_nodes
- def get_intra_layer_edges(self):
- """Return a list with the intra-layer edges"""
- return self.intra_layer_edges
- def get_intra_layer_edges_of_layer(self, layer=0):
- """Return a list with the intra-layer edges of layer"""
- edge_list = self.get_layer(layer).edges()
- # liste of previous layer
- past = [self.num_nodes_in_layers[i] for i in range(layer)]
- # number of previous nodes
- num_past = sum(past)
- elist = []
- for i, j in edge_list:
- elist.append((num_past + i, num_past + j))
- return elist
- def get_inter_layer_edges(self):
- """Return a list with the inter-layer edges"""
- return self.inter_layer_edges
- def get_list_of_layers(self):
- """Return a list with the graphs of the layers"""
- return self.list_of_layers
- def get_layer(self, layer_number):
- """Return the networkx graph of the layer layer_number"""
- return self.list_of_layers[layer_number]
- def set_edges_weights(
- self, intra_layer_edges_weight=None, inter_layer_edges_weight=None
- ):
- """Set the weights of the MultilayerGraph edges
- ---
- intra_layer_edges_weight
- inter_layer_edges_weight
- ---
- Set the "intra_layer_edges_weight" and "inter_layer_edges_weight"
- as an edge attribute with the name "weight"
- """
- if intra_layer_edges_weight is not None:
- self.add_edges_from(self.intra_layer_edges, weight=intra_layer_edges_weight)
- if inter_layer_edges_weight is not None:
- self.add_edges_from(self.inter_layer_edges, weight=inter_layer_edges_weight)
- def set_intra_edges_weights(self, layer=0, weight=None):
- """Set the weights of the MultilayerGraph edges
- ---
- intra_layer_edges_weight
- ---
- Set the "intra_layer_edges_weight" and "intra_layer_edges_weight"
- as an edge attribute with the name "weight"
- """
- elist = self.get_intra_layer_edges_of_layer(layer=layer)
- self.add_edges_from(elist, weight=weight)
- def info(self):
- """Returns some information of the object MultilayerGraph"""
- info = "{}-layer graph,\
- intra_layer_edges:{},\
- inter_layer_edges:{},\
- number_of_nodes_in_layer:{} ".format(
- len(self.list_of_layers),
- len(self.intra_layer_edges),
- len(self.inter_layer_edges),
- self.num_nodes_in_layers,
- )
- return info
multilayer.py at commit 0f1d808, no license · at the source
Overview
and 18 other authors
Einar A Høgestøl25,26,27, Sara Llufriu28, Eloy Martinez-Heras28, Elisabeth Solana28, Silvia Messina29, Marcello Moccia3,30, Gro O Nygaard25,27, Jacqueline Palace29, Daniela Pinter18, Mara A Rocca19,20,23, Ahmed Toosy3, Paola Valsasina19, Olga Ciccarelli3, Eva M Strijbis2,31, Frederik Barkhof2,3,4,8,32, Menno M Schoonheim1,2, Linda Douw1, MAGNIMS study group32 affiliations
- Department of Anatomy and Neurosciences, Amsterdam Neuroscience, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
- MS Center Amsterdam, Amsterdam Neuroscience, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
- Queen Square Multiple Sclerosis Centre, Department of Neuroinflammation, UCL Queen Square Institute of Neurology, University College London, London, United Kingdom
- Department of Radiology and Nuclear Medicine, MS Center Amsterdam, Amsterdam Neuroscience, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
- Departments of Advanced Biomedical Sciences and Electrical Engineering and Information Technology, University of Naples “Federico II,” Naples, Italy
- Dutch Institute for Emergent Phenomena (DIEP), Institute for Advanced Studies, University of Amsterdam, Amsterdam, The Netherlands
- Department of Psychiatry, Amsterdam Neuroscience, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
- Centre for Medical Image Computing, Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom
- E-Health Center, Universitat Oberta de Catalunya, Barcelona, Spain
- Department of Advanced Medical and Surgical Sciences, University of Campania “Luigi Vanvitelli,” Naples, Italy
- Translational Imaging in Neurology (ThINK) Basel, Department of Biomedical Engineering, Faculty of Medicine, University Hospital Basel and University of Basel, Basel, Switzerland
- Department of Neurology, University Hospital Basel, Basel, Switzerland
- Research Center for Clinical Neuroimmunology and Neuroscience Basel (RC2NB), University Hospital Basel and University of Basel, Basel, Switzerland
- Dipartimento di Scienze della Salute, Università degli Studi di Genova
- Department of Neurosciences, Biomedicine and Movement Sciences, University of Verona, Verona, Italy
- Department of Information Engineering, University of Padova, Padova, Italy
- Department of Medicine, Surgery and Neuroscience, University of Siena, Siena, Italy
- Department of Neurology, Medical University of Graz, Graz, Austria
- Neuroimaging Research Unit, Division of Neuroscience, IRCCS San Raffaele Scientific Institute, Milan, Italy
- Neurology Unit, IRCCS San Raffaele Scientific Institute, Milan, Italy
- Neurorehabilitation Unit, IRCCS San Raffaele Scientific Institute, Milan, Italy
- Neurophysiology Service, IRCCS San Raffaele Scientific Institute, Milan, Italy
- Vita-Salute San Raffaele University, Milan, Italy
- Movement Disorders, Neurostimulation and Neuroimaging, University Medicine Mainz, Mainz, Germany
- Department of Neurology, Oslo University Hospital, Oslo, Norway
- Department of Psychology, University of Oslo, Oslo, Norway
- Institute of Clinical Medicine, University of Oslo, Oslo, Norway
- Neuroimmunology and Multiple Sclerosis Unit and Laboratory of Advanced Imaging in Neuroimmunological Diseases (ImaginEM), Hospital Clinic and Institut d’Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS), University of Barcelona, Barcelona, Spain
- Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, United Kingdom
- Department of Molecular Medicine and Medical Biotechnology, University of Naples “Federico II,” Naples, Italy
- Department of Neurology, MS Center Amsterdam, Amsterdam Neuroscience, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
- Dementia Research Centre, UCL Queen Square Institute of Neurology, University College London, London, United Kingdom
Abstract
People with multiple sclerosis (MS) often present with cognitive deficits that cannot fully be attributed to focal brain alterations. Whole-brain network changes show stronger relations, but MS network insights have mostly focused on either structural or functional (single-layer) networks, while recent work has shown the importance of multilayer frontoparietal network integration for cognition. Here, we explored the cognitive relevance of multilayer integration of the frontoparietal network in relapsing–remitting MS (n = 780) using diffusion and resting-state fMRI. Cognitive relations were first assessed for nodal multilayer eigenvector centrality, averaged over frontoparietal network nodes as a measure of integration, and post hoc for mean eccentricity for both single layer and multilayers. Higher multilayer frontoparietal network centrality was associated with worse Symbol Digit Modalities Test (SDMT) performance (β = −.117, p = .005). Mean eccentricity of single-layer diffusion (β = −.123, p < .001) and multilayer networks (β = .085, p = .018) were associated with SDMT performance. However, results could not be replicated using a different anatomical parcellation. This study showed that cognition in MS is related to multilayer network parameters. Nevertheless, correlations were weak and atlas specific, suggesting that a binary structure–function multilayer network approach is not particularly relevant as a correlate of cognition in MS.
Reproduced under the paper's license (CC BY), from the paper cited above.
Repositories
Its files are read in the Code ↔ Paper reader above, with 2 matches between paragraphs and lines of code.
python.org
Availability: 1 check, the latest on 28 September 2026: the link answers (HTTP 200)
- 28 September 2026: the link answers (HTTP 200)
networkx
Availability: 1 check, the latest on 29 September 2026: the link answers (HTTP 200)
- 29 September 2026: the link answers (HTTP 200)
nkoub/multinetx
0f1d80869cb5ba8138988bd778ec480b9a099268, 5 August 2024Availability: 1 check, the latest on 29 September 2026: the link answers
- 29 September 2026: the link answers
18 files
- examples/
.ipynb_checkpoints/ , Jupyter, 108 linescreate_multiplex-checkpo int.ipynb - examples/
.ipynb_checkpoints/ , Jupyter, 1 linemultiplex_turing_pattern s-checkpoint.ipynb - examples/
.ipynb_checkpoints/ , Jupyter, 1 lineplot_multiplex_networks- checkpoint.ipynb - examples/
.ipynb_checkpoints/ , Jupyter, 1 linespectrum_two_layers-chec kpoint.ipynb - examples/
create_multiplex.ipynb , Jupyter, 108 lines - examples/
dynamics/ , Jupyter, 179 lines.ipynb_checkpoints/ multiplex_turing_pattern s-checkpoint.ipynb - examples/
dynamics/ , Jupyter, 179 linesmultiplex_turing_pattern s.ipynb - examples/
multinetX_test.ipynb , Jupyter, 396 lines - examples/
plot_multiplex_networks. , Jupyter, 165 linesipynb - examples/
spectrum_two_layers.ipyn , Jupyter, 1 lineb - multinetx/
__init__.py , Python, 60 lines, 1 match - multinetx/
core/ , Python, 32 lines__init__.py - multinetx/
core/ , Python, 684 linesdraw.py - multinetx/
core/ , Python, 43 linesexceptions.py - multinetx/
core/ , Python, 266 lines, 1 matchmultilayer.py - multinetx/
core/ , Python, 268 linesutilities.py - setup.py, Python, 45 lines
- README.md, Text, 488 lines
multinetlab-amsterdam
Availability: 1 check, the latest on 29 September 2026: the link answers (HTTP 200)
- 29 September 2026: the link answers (HTTP 200)
The paper's code and data availability statement is in the Data section.
Tracing map
Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.
What the map holds:
- 4 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
- 17 scripts, each with its path and the digest of its content;
- 2 matches between paragraphs of the paper and lines of the code (method lexical-v1);
- neither the text of the paper nor the code itself.
Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.
Data
No dataset and no data link were found in the paper.
Data Availability Statement
The code used for the analyses in this study are available upon request; please contact L.D.
Reproduced under the paper's license (CC BY), from the paper cited above.
Versions
The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.
Version 1, 29 September 2026: the first record
Recorded: type, language, journal, volume, issue, pages, dates, 38 authors, 5 keywords, 68 references.
Cite
This paper
Breedt, L. C., Pontillo, G., Santos, F. A. N., Vriend, C., Prados, F., Wink, A. M., Bisecco, A., Cagol, A., Calabrese, M., Castellaro, M., Collorone, S., Cortese, R., De Stefano, N., Enzinger, C., Filippi, M., Foster, M. A., Gallo, A., Gonzalez-Escamilla, G., Granziera, C., . . . MAGNIMS study group. (2026). Structure-function multilayer network integration and cognition in multiple sclerosis. Network neuroscience (Cambridge, Mass.), 10(2), 400-417. https://
BibTeX
@article{breedt2026struc
author = {Breedt, Lucas C and Pontillo, Giuseppe and Santos, Fernando A N and Vriend, Chris and Prados, Ferran and Wink, Alle Meije and Bisecco, Alvino and Cagol, Alessandro and Calabrese, Massimiliano and Castellaro, Marco and Collorone, Sara and Cortese, Rosa and De Stefano, Nicola and Enzinger, Christian and Filippi, Massimo and Foster, Michael A and Gallo, Antonio and Gonzalez-Escamilla, Gabriel and Granziera, Cristina and Groppa, Sergiu and Høgestøl, Einar A and Llufriu, Sara and Martinez-Heras, Eloy and Solana, Elisabeth and Messina, Silvia and Moccia, Marcello and Nygaard, Gro O and Palace, Jacqueline and Pinter, Daniela and Rocca, Mara A and Toosy, Ahmed and Valsasina, Paola and Ciccarelli, Olga and Strijbis, Eva M and Barkhof, Frederik and Schoonheim, Menno M and Douw, Linda and {MAGNIMS study group}},
title = {{Structure-function multilayer network integration and cognition in multiple sclerosis}},
journal = {Network neuroscience (Cambridge, Mass.)},
year = {2026},
month = apr,
volume = {10},
number = {2},
pages = {400--417},
publisher = {MIT Press},
issn = {2472-1751},
doi = {10.1162/
url = {https://
pmid = {42039096},
pmcid = {PMC13108497}
}
RIS
TY - JOUR
AU - Breedt, Lucas C
AU - Pontillo, Giuseppe
AU - Santos, Fernando A N
AU - Vriend, Chris
AU - Prados, Ferran
AU - Wink, Alle Meije
AU - Bisecco, Alvino
AU - Cagol, Alessandro
AU - Calabrese, Massimiliano
AU - Castellaro, Marco
AU - Collorone, Sara
AU - Cortese, Rosa
AU - De Stefano, Nicola
AU - Enzinger, Christian
AU - Filippi, Massimo
AU - Foster, Michael A
AU - Gallo, Antonio
AU - Gonzalez-Escamilla, Gabriel
AU - Granziera, Cristina
AU - Groppa, Sergiu
AU - Høgestøl, Einar A
AU - Llufriu, Sara
AU - Martinez-Heras, Eloy
AU - Solana, Elisabeth
AU - Messina, Silvia
AU - Moccia, Marcello
AU - Nygaard, Gro O
AU - Palace, Jacqueline
AU - Pinter, Daniela
AU - Rocca, Mara A
AU - Toosy, Ahmed
AU - Valsasina, Paola
AU - Ciccarelli, Olga
AU - Strijbis, Eva M
AU - Barkhof, Frederik
AU - Schoonheim, Menno M
AU - Douw, Linda
AU - MAGNIMS study group
TI - Structure-function multilayer network integration and cognition in multiple sclerosis
T2 - Network neuroscience (Cambridge, Mass.)
J2 - Netw Neurosci
PY - 2026
DA - 2026/
VL - 10
IS - 2
SP - 400
EP - 417
SN - 2472-1751
PB - MIT Press
DO - 10.1162/
UR - https://
LA - en
ER -
CSL-JSON
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