Temporal network, centrality measures, and ordinary differential equations

• Název práce v češtině: Temporal network, centrality measures, and ordinary differential equations
• Název v anglickém jazyce: Temporal network, centrality measures, and ordinary differential equations
• Akademický rok vypsání: 2024/2025
• Typ práce: diplomová práce
• Ústav: Katedra numerické matematiky (32-KNM)
• Vedoucí / školitel: Stefano Pozza, Dr., Ph.D.

Zásady pro vypracování

The thesis consists of testing state-of-the-art methods for identifying the most important nodes in a network. In particular, it will test a new approach based on the solution of ODEs. The thesis will require a literature review and the implementation of several tests in MatLab.

Seznam odborné literatury

- Arrigo F, Higham DJ. Sparse matrix computations for dynamic network centrality. Applied network science. 2017 Dec;2:1-9.
- Arrigo F, Higham DJ, Noferini V, Wood R. Dynamic Katz and related network measures. Linear Algebra and its Applications. 2022 Dec 15;655:159-85.
- Arrigo F, Tudisco F. Multi-dimensional, multilayer, nonlinear and dynamic HITS. In Proceedings of the 2019 SIAM International Conference on Data Mining 2019 May 6 (pp. 369-377). Society for Industrial and Applied Mathematics.
- Benzi M, Boito P. Matrix functions in network analysis. GAMM‐Mitteilungen. 2020 Sep;43(3):e202000012.
- Benzi M, Boito P. Quadrature rule-based bounds for functions of adjacency matrices. Linear Algebra and its Applications. 2010 Sep 1;433(3):637-52.
- Chen I, Benzi M, Chang HH, Hertzberg VS. Dynamic communicability and epidemic spread: a case study on an empirical dynamic contact network. Journal of Complex Networks. 2016 Jun 1;5(2):274-302.
- Estrada E. The structure of complex networks: theory and applications. American Chemical Society; 2012.
- Giscard PL, Lui K, Thwaite SJ, Jaksch D. An exact formulation of the time-ordered exponential using path-sums. Journal of Mathematical Physics. 2015 May 1;56(5).
- Grindrod P, Parsons MC, Higham DJ, Estrada E. Communicability across evolving networks. Physical Review E. 2011 Apr 25;83(4):046120.

Předběžná náplň práce

Complex networks emerge from many applications, from social network analysis to city planning to biotechnology. In particular, identifying relevant information is a crucial task in data analysis and information retrieval that can be solved by relying on the concept of "centrality measure" of a network's nodes. As data is often time-dependent, temporal networks, i.e., networks whose nodes and weights change with time, can also be analyzed using centrality measures. A new approach to solving ODEs has recently been introduced in [Giscard et al., 2015]. This method leads to a natural extension of the so-called subgraph-centrality measures to the temporal case.
This project aims to test and compare the new method with state-of-the-art centrality measures for temporal networks. Moreover, it aims to explain its interpretation in terms of the number of closed walks in the network.

Předběžná náplň práce v anglickém jazyce

Complex networks emerge from many applications, from social network analysis to city planning to biotechnology. In particular, identifying relevant information is a crucial task in data analysis and information retrieval that can be solved by relying on the concept of "centrality measure" of a network's nodes. As data is often time-dependent, temporal networks, i.e., networks whose nodes and weights change with time, can also be analyzed using centrality measures. A new approach to solving ODEs has recently been introduced in [Giscard et al., 2015]. This method leads to a natural extension of the so-called subgraph-centrality measures to the temporal case.
This project aims to test and compare the new method with state-of-the-art centrality measures for temporal networks. Moreover, it aims to explain its interpretation in terms of the number of closed walks in the network.