When simplicial complexes are used to represent higher-order systems, information regarding when and how interactions happen may be lost. In this paper, we propose the concept of temporal simplicial complexes, in which simplices with timestamps (or temporal simplices) are used to represent interactions, and faces with weights are used to represent relations. Then, we propose a growing model with two rules, face dimension selection (FDS), and preferential attachment. By properly setting the probability parameter vector q in the FDS rule, one can balance network diameter expansion and network centrality, thus attaining more flexibility in the growing process. Our theoretical analysis and simulations that followed show the generalized degree of faces of any dimension follows a power-law distribution, with a scaling component controlled by q. Our work provides a flexible growing model and can be used to study higher-order systems with temporal properties.
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October 2024
Research Article|
October 01 2024
Growing simplicial complex with face dimension selection and preferential attachment
Mengjun Ding
;
Mengjun Ding
(Conceptualization, Formal analysis, Methodology, Project administration, Writing – original draft)
School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University
, Shanghai 200241, China
Search for other works by this author on:
Jia Yu
;
Jia Yu
(Methodology, Writing – original draft)
School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University
, Shanghai 200241, China
Search for other works by this author on:
Weiqiang Sun
Weiqiang Sun
a)
(Conceptualization, Formal analysis, Funding acquisition, Project administration, Writing – original draft)
School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University
, Shanghai 200241, China
a)Author to whom correspondence should be addressed: sunwq@sjtu.edu.cn
Search for other works by this author on:
a)Author to whom correspondence should be addressed: sunwq@sjtu.edu.cn
Chaos 34, 103107 (2024)
Article history
Received:
March 28 2024
Accepted:
September 09 2024
Citation
Mengjun Ding, Jia Yu, Weiqiang Sun; Growing simplicial complex with face dimension selection and preferential attachment. Chaos 1 October 2024; 34 (10): 103107. https://doi.org/10.1063/5.0210960
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