A multi-class approach for ranking graph nodes: models and experiments with incomplete data

TL;DR

This paper introduces models and algorithms for ranking nodes in multi-parameter graphs, addressing stability, convergence, and robustness with incomplete data, applicable across various network types.

Contribution

It presents new models and numerical algorithms for multi-parameter graph ranking, analyzing their stability, convergence, and robustness with incomplete data.

Findings

Models achieve up to 60% correlation with full data rankings using only 10% of attribute links.

Algorithms are fast, stable, and adaptable to different network types.

Robustness analysis shows effective ranking even with incomplete data.

Abstract

After the phenomenal success of the PageRank algorithm, many researchers have extended the PageRank approach to ranking graphs with richer structures beside the simple linkage structure. In some scenarios we have to deal with multi-parameters data where each node has additional features and there are relationships between such features. This paper stems from the need of a systematic approach when dealing with multi-parameter data. We propose models and ranking algorithms which can be used with little adjustments for a large variety of networks (bibliographic data, patent data, twitter and social data, healthcare data). In this paper we focus on several aspects which have not been addressed in the literature: (1) we propose different models for ranking multi-parameters data and a class of numerical algorithms for efficiently computing the ranking score of such models, (2) by analyzing the stability and convergence properties of the numerical schemes we tune a fast and stable technique for the ranking problem, (3) we consider the issue of the robustness of our models when data are incomplete. The comparison of the rank on the incomplete data with the rank on the full structure shows that our models compute consistent rankings whose correlation is up to 60% when just 10% of the links of the attributes are maintained suggesting the suitability of our model also when the data are incomplete.