Bridging The Scales in Network Science
Lead Research Organisation:
University of Oxford
Department Name: Mathematical Institute
Abstract
A variety of systems of current scientific interest can be represented as networks. Important examples can be drawn from neuroscience, the social sciences and engineering, to name a few.
The study of such real-world networks has triggered the development of metrics and algorithms to extract information from large-scale networked systems, answering questions such as: What are the central nodes? Are there groups of nodes that play a similar role? How does the network structure affect diffusive dynamics, for example, epidemic spreading?
The central research theme aims at understanding the relationship between the local properties of a graph, typically described by the direct neighbourhood of a node, and its global properties, such as different measures of the "size" of the graph. A good example is given by the design of random graphs, where local properties are constrained, such as in the configuration model, and one aims to be able to predict the resulting properties of the graph at different scales.
The main purpose of this project will be to explore the relations between these scales, and to identify intermediate scales of description. This problem, related to community detection, will be investigated by looking at the dynamics of signed networks, which model systems where there can be two opposing types of relationships between nodes, and will focus on the relation between structural imbalance and the emergence of polarization. The project will also investigate multi-scale measures of centrality and clustering, capturing the role of a node within certain regions of a graph. This methodological project will be tested and inspired by real-world network datasets, and aims at deepening our mathematical knowledge of graph node importance across various scales. The project finds connections to model order reduction and to network block models, and will involve a combination of data mining, mathematical modelling and numerical simulations.
The project falls within the EPSRC research areas of non-linear systems, statistics and applied probability and mathematical analysis.
The study of such real-world networks has triggered the development of metrics and algorithms to extract information from large-scale networked systems, answering questions such as: What are the central nodes? Are there groups of nodes that play a similar role? How does the network structure affect diffusive dynamics, for example, epidemic spreading?
The central research theme aims at understanding the relationship between the local properties of a graph, typically described by the direct neighbourhood of a node, and its global properties, such as different measures of the "size" of the graph. A good example is given by the design of random graphs, where local properties are constrained, such as in the configuration model, and one aims to be able to predict the resulting properties of the graph at different scales.
The main purpose of this project will be to explore the relations between these scales, and to identify intermediate scales of description. This problem, related to community detection, will be investigated by looking at the dynamics of signed networks, which model systems where there can be two opposing types of relationships between nodes, and will focus on the relation between structural imbalance and the emergence of polarization. The project will also investigate multi-scale measures of centrality and clustering, capturing the role of a node within certain regions of a graph. This methodological project will be tested and inspired by real-world network datasets, and aims at deepening our mathematical knowledge of graph node importance across various scales. The project finds connections to model order reduction and to network block models, and will involve a combination of data mining, mathematical modelling and numerical simulations.
The project falls within the EPSRC research areas of non-linear systems, statistics and applied probability and mathematical analysis.
Organisations
People |
ORCID iD |
| Radek Erban (Primary Supervisor) | |
| Shazia'Ayn Babul (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/W523781/1 | 01/10/2021 | 30/09/2025 | |||
| 2580834 | Studentship | EP/W523781/1 | 01/10/2021 | 30/09/2025 | Shazia'Ayn Babul |