Knotty-centrality: finding the connective core of a complex network

Area of Science:

• Network science
• Graph theory
• Neuroscience

Background:

• Understanding network structure is crucial for analyzing complex systems.
• Identifying central, densely connected components within networks can reveal key organizational principles.

Purpose of the Study:

• To introduce a novel network measure, knotty-centrality, for quantifying topologically central connective cores.
• To define the 'knotty centre' of a network as the subgraph with maximal knotty-centrality.
• To explore the cognitive implications of such connective cores.

Main Methods:

• Definition of knotty-centrality as a measure of intra-connectedness and topological centrality within a node subset.
• Development of a heuristic algorithm to identify network subsets exhibiting high knotty-centrality.
• Application of the algorithm to existing brain structural connectivity datasets (human and cat) and other network types.

Main Results:

• The knotty-centrality measure effectively quantifies the density and centrality of subgraph cores.
• The heuristic algorithm successfully identified high knotty-centrality subgraphs in various networks.
• Analysis of brain connectivity data revealed specific network cores with high knotty-centrality.

Conclusions:

• Knotty-centrality provides a valuable tool for dissecting network architecture.
• The identified connective cores in brain networks may have significant functional and cognitive relevance.
• Further research is warranted to fully elucidate the cognitive implications of these network cores.