Using higher-order Markov models to reveal flow-based communities in networks.

Area of Science:

• Complex Systems Science
• Network Science
• Data Science

Background:

• Complex systems are often modeled as networks with dynamic nodes and edge-mediated interactions.
• Markov processes, like random walks, are common but oversimplify real-world dynamics by lacking memory.
• Real-world systems often exhibit memory effects not captured by simple Markovian models.

Purpose of the Study:

• To enrich network dynamics modeling by incorporating memory using second-order Markov models.
• To generalize standard network algorithms for community detection by extracting novel temporal information.
• To investigate community structures in temporal networks shaped by system correlations.

Main Methods:

• Exploiting empirical pathway information to develop second-order Markov models.
• Generalizing existing network algorithms to incorporate temporal dynamics and memory.
• Applying the methodology to temporal networks to identify time-dependent communities.

Main Results:

• Demonstrated that second-order Markov models can extract novel temporal information from complex systems.
• Successfully uncovered communities in temporal networks based on temporal correlations.
• Showcased the ability to generalize standard network algorithms for enhanced analysis.

Conclusions:

• Second-order Markov models provide a more realistic framework for modeling network dynamics with memory.
• The proposed methodology enhances community detection by leveraging temporal information and correlations.
• This approach offers new insights into the structure and evolution of complex and temporal networks.