Load distribution in weighted complex networks

Area of Science:

• Network Science
• Statistical Physics
• Complex Systems

Background:

• Understanding load distribution is crucial for network robustness and efficiency.
• Optimal paths in weighted networks depend on cost distribution functions.
• Disorder in networks significantly impacts transport properties.

Purpose of the Study:

• To investigate load distribution in weighted networks.
• To determine how network topology (Erdös-Rényi vs. scale-free) affects load distribution.
• To analyze the relationship between local structure (vertex degree) and global transport properties.

Main Methods:

• Measuring the effective number of optimal paths through vertices.
• Analyzing load distribution in Erdös-Rényi (ER) and scale-free (SF) networks under strong disorder.
• Calculating the correlation coefficient between vertex degree and load.

Main Results:

• Load distribution follows a power law in both ER and SF networks in the strong disorder limit.
• Network characteristics are determined by the minimum spanning tree structure.
• Global transport properties are not correlated with local structural information (vertex degree).
• The effect of disorder is larger in ER networks compared to SF networks.

Conclusions:

• The minimum spanning tree structure dictates load distribution characteristics in weighted networks.
• Local network topology does not directly correlate with global transport properties.
• Scale-free networks exhibit different disorder effects compared to random networks.