Black Hole Metric: Overcoming the PageRank Normalization Problem

Abstract In network science, there is often the need to sort the graph nodes. While the sorting strategy may be different, in general sorting is performed by exploiting the network structure. In particular, the metric PageRank has been used in the past decade in different ways to produce a ranking based on how many neighbours point to a specific node. PageRank is simple, easy to compute and effective in many applications, however it comes with a price: as PageRank is an application of the random walker, the arc weights need to be normalized. This normalization, while necessary, introduces a series of unwanted side-effects. In this paper, we propose a generalization of PageRank named Black Hole Metric which mitigates the problem. We devise a scenario in which the side-effects are particularily impactful on the ranking, test the new metric in both real and synthetic networks, and show the results.

[1]  Shlomo Moran,et al.  SALSA: the stochastic approach for link-structure analysis , 2001, TOIS.

[2]  Vincenza Carchiolo,et al.  Reliable peers and useful resources: Searching for the best personalised learning path in a trust- and recommendation-aware environment , 2010, Inf. Sci..

[3]  Punam Bedi,et al.  Empowering recommender systems using trust and argumentation , 2014, Inf. Sci..

[4]  Akbar Ghaffarpour Rahbar,et al.  PowerTrust: A Robust and Scalable Reputation System for Trusted Peer-to-Peer Computing , 2007, IEEE Transactions on Parallel and Distributed Systems.

[5]  Hector Garcia-Molina,et al.  The Eigentrust algorithm for reputation management in P2P networks , 2003, WWW '03.

[6]  Luca Pretto,et al.  A Theoretical Analysis of Google's PageRank , 2002, SPIRE.

[7]  Wenpu Xing,et al.  Weighted PageRank algorithm , 2004, Proceedings. Second Annual Conference on Communication Networks and Services Research, 2004..

[8]  Matthew Richardson,et al.  The Intelligent surfer: Probabilistic Combination of Link and Content Information in PageRank , 2001, NIPS.

[9]  Vincenza Carchiolo,et al.  Users' attachment in trust networks: reputation vs. effort , 2013, Int. J. Bio Inspired Comput..

[10]  K. Duraiswamy,et al.  Comparative Analysis of Different Page Ranking Algorithms , 2015 .

[11]  Allan Borodin,et al.  Perturbation of the Hyper-Linked Environment , 2003, COCOON.

[12]  Stephen Marsh,et al.  Formalising Trust as a Computational Concept , 1994 .

[13]  Pavel Berkhin,et al.  A Survey on PageRank Computing , 2005, Internet Math..

[14]  Vincenza Carchiolo,et al.  Trust assessment: a personalized, distributed, and secure approach , 2012, Concurr. Comput. Pract. Exp..

[15]  Paolo Massa,et al.  Bowling Alone and Trust Decline in Social Network Sites , 2009, 2009 Eighth IEEE International Conference on Dependable, Autonomic and Secure Computing.

[16]  Enrique Herrera-Viedma,et al.  A google wave-based fuzzy recommender system to disseminate information in University Digital Libraries 2.0 , 2011, Inf. Sci..

[17]  Yolanda Gil,et al.  A survey of trust in computer science and the Semantic Web , 2007, J. Web Semant..

[18]  Shaozhi Ye,et al.  Distributed PageRank computation based on iterative aggregation-disaggregation methods , 2005, CIKM '05.

[19]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[20]  Dima Shepelyansky,et al.  Two-dimensional ranking of Wikipedia articles , 2010, ArXiv.

[21]  Béla Bollobás,et al.  Directed scale-free graphs , 2003, SODA '03.

[22]  Ashutosh Kumar Singh,et al.  A Comparative Study of Page Ranking Algorithms for Information Retrieval , 2009 .

[23]  Li Chen,et al.  Recommender systems based on user reviews: the state of the art , 2015, User Modeling and User-Adapted Interaction.

[24]  Jimmy J. Lin,et al.  WTF: the who to follow service at Twitter , 2013, WWW.

[25]  José Angel Olivas,et al.  Hiperion: A fuzzy approach for recommending educational activities based on the acquisition of competences , 2013, Inf. Sci..

[26]  Lea Kutvonen,et al.  Trust Management Survey , 2005, iTrust.

[27]  M. Den Besten.  The PageRank Problem , 2010 .

[28]  Albert Y. Zomaya,et al.  The Pagerank-Index: Going beyond Citation Counts in Quantifying Scientific Impact of Researchers , 2015, PloS one.

[29]  Vincenza Carchiolo,et al.  Searching for experts in a context-aware recommendation network , 2015, Comput. Hum. Behav..

[30]  Vincenza Carchiolo,et al.  Gain the Best Reputation in Trust Networks , 2011, IDC.

[31]  David F. Gleich,et al.  PageRank beyond the Web , 2014, SIAM Rev..

[32]  Azadeh Shakery,et al.  DirichletRank: Solving the zero-one gap problem of PageRank , 2008, TOIS.

[33]  Carl D. Meyer,et al.  Deeper Inside PageRank , 2004, Internet Math..

[34]  Rajeev Motwani,et al.  The PageRank Citation Ranking : Bringing Order to the Web , 1999, WWW 1999.

[35]  Ling Liu,et al.  PeerTrust: supporting reputation-based trust for peer-to-peer electronic communities , 2004, IEEE Transactions on Knowledge and Data Engineering.

[36]  Marc Najork,et al.  Comparing the effectiveness of hits and salsa , 2007, CIKM '07.

[37]  Dong Xin,et al.  Fast personalized PageRank on MapReduce , 2011, SIGMOD '11.

[38]  Vincenza Carchiolo,et al.  Trusting Evaluation by Social Reputation , 2008, IDC.

[39]  F. Soleymani,et al.  PageRank Problem, Survey And Future Research Directions , 2010 .

[40]  N. L. Chervany,et al.  THE MEANINGS OF TRUST , 2000 .

[41]  Young Ae Kim,et al.  A trust prediction framework in rating-based experience sharing social networks without a Web of Trust , 2012, Inf. Sci..

[42]  Miguel-Ángel Sicilia,et al.  A survey of approaches for ranking on the web of data , 2014, Information Retrieval.

[43]  Ashish Goel,et al.  Fast Incremental and Personalized PageRank , 2010, Proc. VLDB Endow..

[44]  Jérôme Kunegis,et al.  KONECT: the Koblenz network collection , 2013, WWW.

[45]  Franco Scarselli,et al.  Inside PageRank , 2005, TOIT.