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Modeling the Functional Network for Spatial Navigation in the Human Brain
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Published on: October 13, 2023

Fast computing betweenness centrality with virtual nodes on large sparse networks.

Jing Yang1, Yingwu Chen

  • 1Department of Information Systems and Management, National University of Defense Technology, Changsha, China. jing_edu@sohu.com

Plos One
|August 6, 2011
PubMed
Summary
This summary is machine-generated.

Calculating betweenness centrality for complex networks is slow. A new algorithm using virtual nodes and breadth-first search (BFS) offers a faster method for large, lightly weighted networks.

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Area of Science:

  • Network Science
  • Graph Theory
  • Computer Science

Background:

  • Betweenness centrality is a crucial metric for analyzing complex networks.
  • Existing algorithms for betweenness centrality are computationally intensive, particularly for weighted networks, with a time complexity of O(N(M + N log N)).

Purpose of the Study:

  • To develop a more efficient algorithm for calculating betweenness centrality in complex networks.
  • To reduce the computational time required for betweenness centrality analysis, especially in large-scale networks.

Main Methods:

  • Proposed an algorithm that inserts virtual nodes into weighted edges.
  • Transformed the shortest path problem into a breadth-first search (BFS) problem.
  • Achieved a time complexity of O(wDN2) for integer-weighted networks, where w is the average edge weight and D is the average node degree.

Main Results:

  • The new algorithm significantly saves computation time when the average edge weight (w) is less than (log N/D + 1).
  • Demonstrated suitability for analyzing large, sparse, and lightly weighted networks.
  • Validated the algorithm's feasibility through numerical simulations on diverse random networks.

Conclusions:

  • The proposed virtual node transformation method provides an efficient alternative for computing betweenness centrality.
  • This approach is applicable to other shortest path-based network indices, such as closeness and stress centrality.
  • The algorithm is a practical tool for large network analysis, offering substantial time savings under specific network conditions.