Reconstructing complex networks without time series.

Area of Science:

• Network science
• Complex systems
• Data analysis

Background:

• Real-world network dynamics are often transient, leaving only final nodal states as data.
• Traditional network reconstruction methods typically require time-series data, which may not always be available.

Purpose of the Study:

• To develop a framework for reconstructing network topology from non-time-series data, specifically final nodal states.
• To investigate the feasibility of inferring network interactions from the outcomes of spreading processes.

Main Methods:

• A maximum likelihood estimation (MLE)-based framework was developed to infer interaction topology.
• The framework was tested using ensembles of final nodal states from statistically independent initial triggers.
• Mathematical theory was derived and validated using diverse spreading dynamics and real-world network topologies.

Main Results:

• Network topology can be accurately reconstructed solely from binary final nodal states for certain dynamical processes.
• Incorporating first arrival time data enhances reconstruction accuracy.
• Network reconstruction is feasible even for processes with uniform final states by utilizing first arrival times.

Conclusions:

• The proposed framework offers a robust method for network topology reconstruction from static, non-time-series data.
• This approach is valuable for analyzing transient network dynamics where only final states are observable.
• The study demonstrates the power of leveraging outcome data for inferring underlying network structures.