Stability of Consensus Node Orderings Under Imperfect Network Data

In complex network analysis, the problem of ranking individual nodes based on their importance has attracted increasing attention from the scientific community due to its vast application, such as identification of influential spreaders for viral marketing or epidemic control, bottlenecks for traffic congestion control, and so on. The growing literature proposes a number of measures to determine the rank order of the network entities where complete information about the nodes and their interaction is available. Degree centrality, PageRank, eigenvector centrality, closeness centrality are few such popular measures. In most real-life scenarios, however, the information about the underlying network is incomplete or affected due to noise. The few works that study the effects of incomplete information on the rank orders show the vulnerability of the rank orders in various topologies. In this paper, we investigate the effects of noise, both random and nonrandom, on the aggregated rank orders determined from the degree, PageRank, eigenvector centrality, and closeness centrality-based rankings. This paper reveals an important insight that even the simple Borda Count ranking has the potential to improve on the accuracy of rank orders in networks with uncertainty. This paper shows the existence of stable nodes in various networks and indicates that the design of the consensus approach based on the properties of the stable nodes can further improve the stability of the rank orders.

[1]  L. Freeman.  Centrality in social networks conceptual clarification , 1978 .

[2]  Jacob L. Moreno,et al.  Who shall survive? : foundations of sociometry, group psychotherapy, and sociodrama , 1953 .

[3]  Jure Leskovec,et al.  Measurement error in network data: A re-classification , 2012, Soc. Networks.

[4]  Amy Nicole Langville,et al.  Google's PageRank and beyond - the science of search engine rankings , 2006 .

[5]  Rushed Kanawati,et al.  Supervised rank aggregation approach for link prediction in complex networks , 2012, WWW.

[6]  Jennifer Golbeck,et al.  Analyzing the Social Web , 2013 .

[7]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .

[8]  Mark Huisman,et al.  Treatment of non-response in longitudinal network studies , 2008, Soc. Networks.

[9]  Paul J. Laurienti,et al.  Changes in Cognitive State Alter Human Functional Brain Networks , 2011, Front. Hum. Neurosci..

[10]  O. Sporns.  Structure and function of complex brain networks , 2013, Dialogues in clinical neuroscience.

[11]  Yicheng Zhang,et al.  Identifying influential nodes in complex networks , 2012 .

[12]  James Moody,et al.  Structural effects of network sampling coverage I: Nodes missing at random , 2013, Soc. Networks.

[13]  S. Mahadevan,et al.  Identifying influential nodes in weighted networks based on evidence theory , 2013 .

[14]  Ronald Fagin,et al.  Comparing and aggregating rankings with ties , 2004, PODS '04.

[15]  R. Burt,et al.  Applied Network Analysis: A Methodological Introduction , 1983 .

[16]  P.-C.-F. Daunou,et al.  Mémoire sur les élections au scrutin , 1803 .

[17]  Alex Bavelas,et al.  Communication Patterns in Task‐Oriented Groups , 1950 .

[18]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[19]  John Scott,et al.  The SAGE Handbook of Social Network Analysis , 2011 .

[20]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[21]  Umberto Straccia,et al.  Web metasearch: rank vs. score based rank aggregation methods , 2003, SAC '03.

[22]  Duanbing Chen,et al.  Identifying Influential Spreaders by Weighted LeaderRank , 2013, ArXiv.

[23]  Masahiro Kimura,et al.  Extracting influential nodes on a social network for information diffusion , 2009, Data Mining and Knowledge Discovery.

[24]  Yu Zhang,et al.  Identifying Key Users for Targeted Marketing by Mining Online Social Network , 2010, 2010 IEEE 24th International Conference on Advanced Information Networking and Applications Workshops.

[25]  S. Shapiro,et al.  Mathematics without Numbers , 1993 .

[26]  L. Fleming,et al.  Collaborative Brokerage, Generative Creativity, and Creative Success , 2007 .

[27]  Moni Naor,et al.  Rank aggregation methods for the Web , 2001, WWW '01.

[28]  Pan-Jun Kim,et al.  Reliability of rank order in sampled networks , 2005, physics/0702148.

[29]  Yi-Cheng Zhang,et al.  Leaders in Social Networks, the Delicious Case , 2011, PloS one.

[30]  Pablo A. Estévez,et al.  Selecting the Most Influential Nodes in Social Networks , 2007, 2007 International Joint Conference on Neural Networks.

[31]  W. C. Carter,et al.  Detecting measurement bias in respondent reports of personal networks , 2002, Soc. Networks.

[32]  William Richards,et al.  Nonrespondents in Communication Network Studies , 1992 .

[33]  M. Newman.  1 Who is the best connected scientist ? A study of scientific coauthorship networks , 2004 .

[34]  Lev Muchnik,et al.  Identifying influential spreaders in complex networks , 2010, 1001.5285.

[35]  Gert Sabidussi,et al.  The centrality index of a graph , 1966 .

[36]  J. Kleinberg.  Algorithmic Game Theory: Cascading Behavior in Networks: Algorithmic and Economic Issues , 2007 .

[37]  Prem Melville,et al.  Supervised Rank Aggregation for Predicting Influence in Networks , 2011, ArXiv.

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

[39]  Yiping Yao,et al.  Identifying all-around nodes for spreading dynamics in complex networks , 2012 .

[40]  M. Kendall.  A NEW MEASURE OF RANK CORRELATION , 1938 .

[41]  Linyuan Lu,et al.  Uncovering missing links with cold ends , 2011, ArXiv.

[42]  Marián Boguñá,et al.  How to make the top ten: Approximating PageRank from in-degree , 2005, ArXiv.

[43]  Pierre Azoulay,et al.  Peer effects in the workplace: evidence from professional transitions for the superstars of medicine , 2006 .

[44]  Cristopher Moore,et al.  Accuracy and scaling phenomena in Internet mapping. , 2004, Physical review letters.

[45]  Sergey Brin,et al.  Reprint of: The anatomy of a large-scale hypertextual web search engine , 2012, Comput. Networks.

[46]  Phillip Bonacich,et al.  Eigenvector-like measures of centrality for asymmetric relations , 2001, Soc. Networks.

[47]  Gourab Ghoshal,et al.  Ranking stability and super-stable nodes in complex networks. , 2011, Nature communications.

[48]  Florian Probst,et al.  Identifying Key Users in Online Social Networks: A PageRank Based Approach , 2010, ICIS.

[49]  Gueorgi Kossinets.  Effects of missing data in social networks , 2006, Soc. Networks.

[50]  Thomas W. Valente,et al.  The stability of centrality measures when networks are sampled , 2003, Soc. Networks.

[51]  Tomasz Arodz,et al.  Identifying influential nodes in a wound healing-related network of biological processes using mean first-passage time , 2015 .

[52]  Qilin Li,et al.  A scoring mechanism for the rank aggregation of network robustness , 2013, Commun. Nonlinear Sci. Numer. Simul..

[53]  Mark Gerstein,et al.  The Importance of Bottlenecks in Protein Networks: Correlation with Gene Essentiality and Expression Dynamics , 2007, PLoS Comput. Biol..

[54]  Terrill L. Frantz,et al.  Robustness of centrality measures under uncertainty: Examining the role of network topology , 2009, Comput. Math. Organ. Theory.

[55]  Alain Denise,et al.  Rank aggregation with ties: Experiments and Analysis , 2015, Proc. VLDB Endow..

[56]  Sangwook Kim,et al.  Identifying and ranking influential spreaders in complex networks by neighborhood coreness , 2014 .

[57]  Kathleen M. Carley,et al.  On the robustness of centrality measures under conditions of imperfect data , 2006, Soc. Networks.

[58]  Steven B. Andrews,et al.  Structural Holes: The Social Structure of Competition , 1995, The SAGE Encyclopedia of Research Design.

[59]  S. Mahadevan,et al.  A modified evidential methodology of identifying influential nodes in weighted networks , 2013 .

[60]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[61]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.