# Effect of node deleting on network structure

## TL;DR

This paper investigates how node deletion affects network structure, revealing transitions from scale-free to exponential degree distributions, development of disassortative correlations, and impacts on connectivity and clustering.

## Contribution

It introduces a new network growth model incorporating node deletion, providing insights into structural transformations and stability of evolving networks.

## Key findings

- Degree distribution shifts from scale-free to exponential with increased node deletion
- Disassortative degree correlation emerges naturally during evolution
- Node deletion does not break network connectivity if edge growth is sufficient

## Abstract

The ever-increasing knowledge of the structure of various real-world networks has uncovered their complex multi-mechanism-governed evolution processes. Therefore, a better understanding of the structure and evolution of these networked complex systems requires us to describe such processes in a more detailed and realistic manner. In this paper, we introduce a new type of network growth rule which comprises addition and deletion of nodes, and propose an evolving network model to investigate the effect of node deleting on network structure. It is found that, with the introduction of node deleting, network structure is significantly transformed. In particular, degree distribution of the network undergoes a transition from scale-free to exponential forms as the intensity of node deleting increases. At the same time, nontrivial disassortative degree correlation develops spontaneously as a natural result of network evolution in the model. We also demonstrate that node deleting introduced in the model does not destroy the connectedness of a growing network so long as the increasing rate of edges is not excessively small. In addition, it is found that node deleting will weaken but not eliminate the small-world effect of a growing network, and generally it will decrease the clustering coefficient in a network.