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Simplicial Activity Driven Model.

Giovanni Petri1, Alain Barrat1,2

  • 1ISI Foundation, 10126 Turin, Italy.

Physical Review Letters
|December 15, 2018
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Summary
This summary is machine-generated.

This study introduces a new model for temporal networks using simplicial complexes to represent multi-agent interactions. This approach reveals crucial differences in network structure and contagion processes compared to traditional models.

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Area of Science:

  • Complex systems science
  • Network science
  • Mathematical modeling

Background:

  • Complex systems are often modeled as networks of pairwise interactions (nodes and links).
  • Many real-world systems, particularly in biology and social sciences, involve interactions among more than two elements.
  • These interactions are frequently dynamic and change over time.

Purpose of the Study:

  • To propose a novel framework, the simplicial activity driven model, for modeling the evolution of temporal networks with multi-agent interactions.
  • To analyze the structural and dynamic differences between simplicial complexes and traditional binary interaction networks.
  • To investigate the impact of simplicial structures on contagion processes like disease or social spread.

Main Methods:

  • Development of the simplicial activity driven model, using simplices (multi-node interactions) as the basic building blocks.
  • Analytical and numerical simulations to compare the proposed model with existing activity driven models (binary interactions).
  • Analysis of paradigmatic contagion processes (e.g., disease propagation) on both network types.

Main Results:

  • The use of simplicial structures leads to significant structural differences compared to traditional activity driven models.
  • The evolution of multi-agent interactions impacts the outcomes of contagion processes.
  • Fluctuations in the number of interacting nodes can alter simple contagion outcomes, unlike in binary interaction models.

Conclusions:

  • Simplicial complexes provide a more adequate representation for complex systems with multi-agent interactions.
  • The proposed simplicial activity driven model offers new insights into the dynamics of temporal networks and contagion.
  • Understanding multi-agent interactions is crucial for accurately modeling phenomena like disease spread in complex systems.