Keith Smith1, Javier Escudero2. 1. Institute for Digital Communications, School of Engineering, University of Edinburgh, West Mains Rd, Edinburgh EH9 3FB, UK; Alzheimer Scotland Dementia Research Centre, University of Edinburgh, 7 George Square, Edinburgh EH8 9JZ, UK. Electronic address: k.smith@ed.ac.uk. 2. Institute for Digital Communications, School of Engineering, University of Edinburgh, West Mains Rd, Edinburgh EH9 3FB, UK. Electronic address: javier.escudero@ed.ac.uk.
Abstract
BACKGROUND: Understanding the complex hierarchical topology of functional brain networks is a key aspect of functional connectivity research. Such topics are obscured by the widespread use of sparse binary network models which are fundamentally different to the complete weighted networks derived from functional connectivity. NEW METHODS: We introduce two techniques to probe the hierarchical complexity of topologies. Firstly, a new metric to measure hierarchical complexity; secondly, a Weighted Complex Hierarchy (WCH) model. To thoroughly evaluate our techniques, we generalise sparse binary network archetypes to weighted forms and explore the main topological features of brain networks - integration, regularity and modularity - using curves over density. RESULTS: By controlling the parameters of our model, the highest complexity is found to arise between a random topology and a strict 'class-based' topology. Further, the model has equivalent complexity to EEG phase-lag networks at peak performance. COMPARISON TO EXISTING METHODS: Hierarchical complexity attains greater magnitude and range of differences between different networks than the previous commonly used complexity metric and our WCH model offers a much broader range of network topology than the standard scale-free and small-world models at a full range of densities. CONCLUSIONS: Our metric and model provide a rigorous characterisation of hierarchical complexity. Importantly, our framework shows a scale of complexity arising between 'all nodes are equal' topologies at one extreme and 'strict class-based' topologies at the other.
BACKGROUND: Understanding the complex hierarchical topology of functional brain networks is a key aspect of functional connectivity research. Such topics are obscured by the widespread use of sparse binary network models which are fundamentally different to the complete weighted networks derived from functional connectivity. NEW METHODS: We introduce two techniques to probe the hierarchical complexity of topologies. Firstly, a new metric to measure hierarchical complexity; secondly, a Weighted Complex Hierarchy (WCH) model. To thoroughly evaluate our techniques, we generalise sparse binary network archetypes to weighted forms and explore the main topological features of brain networks - integration, regularity and modularity - using curves over density. RESULTS: By controlling the parameters of our model, the highest complexity is found to arise between a random topology and a strict 'class-based' topology. Further, the model has equivalent complexity to EEG phase-lag networks at peak performance. COMPARISON TO EXISTING METHODS: Hierarchical complexity attains greater magnitude and range of differences between different networks than the previous commonly used complexity metric and our WCH model offers a much broader range of network topology than the standard scale-free and small-world models at a full range of densities. CONCLUSIONS: Our metric and model provide a rigorous characterisation of hierarchical complexity. Importantly, our framework shows a scale of complexity arising between 'all nodes are equal' topologies at one extreme and 'strict class-based' topologies at the other.
Authors: Maria Del C Valdés Hernández; Keith Smith; Mark E Bastin; E Nicole Amft; Stuart H Ralston; Joanna M Wardlaw; Stewart J Wiseman Journal: Lupus Date: 2020-12-13 Impact factor: 2.911
Authors: Manuel Blesa; Paola Galdi; Simon R Cox; Gemma Sullivan; David Q Stoye; Gillian J Lamb; Alan J Quigley; Michael J Thrippleton; Javier Escudero; Mark E Bastin; Keith M Smith; James P Boardman Journal: Cereb Cortex Date: 2021-03-05 Impact factor: 5.357
Authors: Keith Smith; Benjamin Ricaud; Nauman Shahid; Stephen Rhodes; John M Starr; Augustin Ibáñez; Mario A Parra; Javier Escudero; Pierre Vandergheynst Journal: Sci Rep Date: 2017-02-10 Impact factor: 4.379
Authors: Keith Smith; Mark E Bastin; Simon R Cox; Maria C Valdés Hernández; Stewart Wiseman; Javier Escudero; Catherine Sudlow Journal: Neuroimage Date: 2019-02-14 Impact factor: 6.556