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Growing simplicial complex with face dimension selection and preferential attachment.

Mengjun Ding1, Jia Yu1, Weiqiang Sun1

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We introduce temporal simplicial complexes to capture interaction timing in higher-order systems. A flexible growing model balances network properties, showing face degrees follow a power-law distribution controlled by a parameter.

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Area of Science:

  • Complex Systems
  • Network Science
  • Data Analysis

Background:

  • Higher-order systems are often modeled using simplicial complexes.
  • Existing models may lose crucial temporal information about interactions.
  • Representing the timing and relationships within complex systems is challenging.

Purpose of the Study:

  • To propose temporal simplicial complexes for modeling systems with time-varying interactions.
  • To introduce a flexible growing model for these temporal networks.
  • To analyze the resulting network properties and their control parameters.

Main Methods:

  • Definition of temporal simplicial complexes with timestamped simplices and weighted faces.
  • Development of a growing model incorporating Face Dimension Selection (FDS) and preferential attachment.
  • Theoretical analysis and simulations to study network growth and properties.

Main Results:

  • The proposed model allows balancing network diameter and centrality via the FDS parameter q.
  • Theoretical analysis and simulations confirm a power-law distribution for generalized face degrees.
  • The scaling exponent in the power-law distribution is controllable by the parameter q.

Conclusions:

  • Temporal simplicial complexes offer a flexible framework for higher-order systems with temporal dynamics.
  • The proposed growing model provides tunable control over network structure.
  • This approach enhances the study of complex systems by incorporating temporal and relational information.