Dynamic computation of network statistics via updating schema.

Area of Science:

• Network Science
• Computational Complexity

Background:

• Calculating network statistics like clustering coefficient and modularity is computationally expensive for large networks.
• Traditional methods require full recalculation upon graph modification (edge/vertex addition).

Purpose of the Study:

• To develop efficient update schemes for network statistics, reducing computational complexity for evolving networks.
• To enable faster tracking of dynamic network behavior and identify critical transitions.

Main Methods:

• Introduced novel update schemes for network statistics including degree distribution, clustering coefficient, assortativity, and modularity.
• Presented evolution methods using a network statistics differential notation.

Main Results:

• Significantly reduced computational complexity for tracking network statistics compared to re-calculation.
• Enabled faster computation of network statistics as the network evolves.
• Provided methods to identify critical changes in network statistics.

Conclusions:

• The proposed update schemes offer a computationally efficient alternative for analyzing large, dynamic networks.
• This approach supports modeling network evolution and predicting critical transitions.
• Facilitates the design of network evolution rules to optimize specific network statistics.