Degree distribution and scaling in the Connecting Nearest Neighbors model

TL;DR

This paper analyzes the CNN model's degree distribution, revealing power-law behavior with variable exponents, and establishes connections between the GCNN model and other random walk and recursive search models.

Contribution

It provides a detailed analysis of the degree distribution in the CNN model and links the GCNN model to existing random walk and recursive search models.

Findings

Degree distribution follows a power law with variable exponents.

The GCNN model corresponds to specific random walk and recursive search models.

The scaling behavior depends on parameter settings.

Abstract

We present a detailed analysis of the Connecting Nearest Neighbors (CNN) model by V\'azquez. We show that the degree distribution follows a power law, but the scaling exponent can vary with the parameter setting. Moreover, the correspondence of the growing version of the Connecting Nearest Neighbors (GCNN) model to the particular random walk model (PRW model) and recursive search model (RS model) is established.