Degree Ranking Using Local Information

TL;DR

This paper introduces local algorithms to estimate a node's degree rank in dynamic networks using minimal samples, enabling efficient analysis without full network data, applicable to both social and random networks.

Contribution

The paper presents novel local algorithms for degree rank estimation that require only 1% of network samples, applicable to real-world and synthetic networks, including Erdős-Rényi models.

Findings

High accuracy in degree rank estimation with 1% sampling

Estimation accuracy decreases for lower-ranked nodes

Methods are effective on both social and random networks

Abstract

Most real world dynamic networks are evolved very fast with time. It is not feasible to collect the entire network at any given time to study its characteristics. This creates the need to propose local algorithms to study various properties of the network. In the present work, we estimate degree rank of a node without having the entire network. The proposed methods are based on the power law degree distribution characteristic or sampling techniques. The proposed methods are simulated on synthetic networks, as well as on real world social networks. The efficiency of the proposed methods is evaluated using absolute and weighted error functions. Results show that the degree rank of a node can be estimated with high accuracy using only $1\%$ samples of the network size. The accuracy of the estimation decreases from high ranked to low ranked nodes. We further extend the proposed methods for random networks and validate their efficiency on synthetic random networks, that are generated using Erd\H{o}s-R\'{e}nyi model. Results show that the proposed methods can be efficiently used for random networks as well.