Dismantling complex networks based on the principal eigenvalue of the adjacency matrix

Area of Science:

• Network Science
• Graph Theory
• Complex Systems Analysis

Background:

• Complex network connectivity relies on a few critical nodes.
• Existing methods struggle to identify multiple influential nodes simultaneously.
• Understanding collective influence is crucial for network analysis.

Purpose of the Study:

• To propose a novel metric, collective influence, for identifying multiple key nodes in complex networks.
• To investigate the relationship between internal coupling and node influence.
• To develop an efficient algorithm for network dismantling based on collective influence.

Main Methods:

• Utilizing matrix spectral theory to define and calculate collective influence.
• Developing a greedy algorithm to optimize collective influence for network dismantling.
• Comparing the proposed method against state-of-the-art techniques.

Main Results:

• Identified that highly coupled nodes may have reduced collective influence.
• The proposed greedy algorithm effectively dismantles complex networks.
• Experimental results demonstrate superior performance in terms of principal eigenvalue and giant component reduction.

Conclusions:

• Collective influence offers a robust measure for identifying multiple influential nodes.
• The proposed algorithm provides an effective strategy for complex network dismantling.
• This work advances the understanding and manipulation of complex network structures.