Temporal correlation coefficient for directed networks.

Area of Science:

• Network theory and analysis
• Dynamic systems modeling
• Supply chain management

Background:

• Traditional network analysis often aggregates data over static time windows, losing valuable dynamic information.
• Existing temporal correlation coefficients are limited to undirected networks, failing to capture edge directionality.
• Understanding temporal network dynamics is crucial for fields like supply chain analysis.

Purpose of the Study:

• To adapt the temporal correlation coefficient for directed networks.
• To introduce a methodology that distinguishes between ingoing and outgoing edges.
• To demonstrate the importance of edge direction in network analysis using a real-world example.

Main Methods:

• Development of a novel adaptation of the temporal correlation coefficient for directed networks.
• Calculation of the adapted measure on a small example network to illustrate steps.
• Application of the methodology to a real pig trade network dataset.

Main Results:

• The adapted temporal correlation coefficient successfully distinguishes ingoing and outgoing edge patterns.
• Analysis of the pig trade network revealed significant differences in correlation coefficients based on farm type and position in the supply chain.
• Farms at the beginning of the supply chain showed higher outgoing correlation, while farms at the end showed higher ingoing correlation.

Conclusions:

• The adapted temporal correlation coefficient is a valuable tool for assessing the consistency and structural dynamics of directed networks.
• Ignoring edge direction can lead to the loss of critical information in network analysis.
• This methodology enhances the understanding of complex systems by preserving directional network dynamics.