[Paper Review] The Join of Scale-free Network Models

Xiaomin Wang, Bing Yao+1 more|arXiv (Cornell University)|Dec 29, 2015

Complex Network Analysis Techniques3 references3 citations

TL;DR

This paper proposes the domi-join model, a novel network construction method that joins two scale-free networks using their smallest dominating sets to preserve power-law degree distribution and small-world properties. The method reduces redundant operations through optimized joining logic, maintaining key network characteristics such as high clustering and scale-free behavior.

ABSTRACT

We focus on constructing the domi-join model by doing the join operation based on two smallest dominating sets of two network models and analysis the properties of domi-join model, such as power law distribution, small world. Besides, we will import two class of edge-bound growing network models to explain the process of domi-join model. Then we compute the average degree, clustering coefficient, power law distribution of the domi-join model. Finally, we discuss an impressive method for cutting down redundant operation of domi-join model.

Motivation & Objective

• To develop a new network model that combines two scale-free networks while preserving their structural properties.
• To analyze the domi-join model’s power-law distribution, clustering coefficient, and average degree.
• To reduce computational redundancy in the network joining process through structural optimization.
• To demonstrate that the resulting network maintains small-world characteristics and scale-free behavior.

Proposed method

• Construct the domi-join model by performing a join operation on the smallest dominating sets of two scale-free network models.
• Utilize edge-bound growing network models to model and explain the dynamics of the domi-join process.
• Compute key network metrics including average degree, clustering coefficient, and degree distribution.
• Apply optimization techniques to minimize redundant operations during the joining process.
• Analyze structural properties such as power-law distribution and small-world features using analytical and computational methods.
• Validate the model’s behavior through theoretical analysis of degree distribution and clustering.

Experimental results

Research questions

• RQ1 How can two scale-free networks be joined while preserving their power-law degree distribution?
• RQ2 What is the impact of joining via minimal dominating sets on the clustering coefficient and average degree?
• RQ3 Can the domi-join model maintain small-world properties such as high clustering and short path lengths?
• RQ4 What optimization strategies effectively reduce redundant operations during the network joining process?
• RQ5 How do edge-bound growing models help explain the structural evolution of the domi-join model?

Key findings

• The domi-join model successfully preserves a power-law degree distribution, indicating scale-free characteristics.
• The model exhibits a high clustering coefficient, supporting the presence of small-world properties.
• The average degree remains within a stable range, consistent with known scale-free network behavior.
• The proposed optimization method significantly reduces redundant operations during the joining process.
• Theoretical analysis confirms that the domi-join model maintains key topological features of the original networks.
• Edge-bound growing models effectively model and explain the structural dynamics of the domi-join process.