Comparing Personalized Relevance Algorithms for Directed Graphs

TL;DR

This work addresses context-aware node relevance in directed graphs by introducing Cyclerank, a cycle-based relevance scoring method that assesses mutual reachability with a reference node using cycles up to length $K$ and exponential weighting $\sigma(n)=e^{-n}$. It situates Cyclerank among established methods like PageRank, Personalized PageRank, CheiRank, and 2DRank, detailing a formal score $CR_{r, K}(i) = \sum_{n=2}^{K} \sigma(n) \cdot c_{r, n}(i) = \sum_{n=2}^{K} c_{r,n}(i)/e^{n}$ and comparing results on diverse datasets. The authors present an interactive web platform with 50+ pre-loaded graphs from Wikipedia, Twitter, and Amazon, plus dataset upload and algorithm-extension capabilities, enabling algorithm and dataset comparison through a task/permalink workflow. They demonstrate that Cyclerank can reduce bias toward globally central nodes and yield more contextually relevant results across languages and domains, providing a practical tool for graph analysis and insight discovery.

Abstract

We present an interactive Web platform that, given a directed graph, allows identifying the most relevant nodes related to a given query node. Besides well-established algorithms such as PageRank and Personalized PageRank, the demo includes Cyclerank, a novel algorithm that addresses some of their limitations by leveraging cyclic paths to compute personalized relevance scores. Our demo design enables two use cases: (a) algorithm comparison, comparing the results obtained with different algorithms, and (b) dataset comparison, for exploring and gaining insights into a dataset and comparing it with others. We provide 50 pre-loaded datasets from Wikipedia, Twitter, and Amazon and seven algorithms. Users can upload new datasets, and new algorithms can be easily added. By showcasing efficient algorithms to compute relevance scores in directed graphs, our tool helps to uncover hidden relationships within the data, which makes of it a valuable addition to the repertoire of graph analysis algorithms.

Figures (2)

• Figure 1: Architecture of the demonstration
• Figure 2: Task builder interface