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k-Metric Antidimension: a Privacy Measure for Social Graphs [article]

Rolando Trujillo-Rasua, Ismael G. Yero
2015 arXiv   pre-print
In this article, we introduce a novel privacy measure, named (k, ℓ)-anonymity and based on the k-metric antidimension problem, aimed at evaluating the resistance of social graphs to active attacks.  ...  We, therefore, propose a true-biased algorithm for computing the k-metric antidimension of random graphs.  ...  It also introduces the k-metric antidimension as the basis for the privacy measure (k, )-anonymity.  ... 
arXiv:1408.2154v2 fatcat:5tlnqmeh5ncy7agx4d4xhxa25u

k -Metric antidimension: A privacy measure for social graphs

Rolando Trujillo-Rasua, Ismael G. Yero
2016 Information Sciences  
In this article, we introduce (k, )-anonymity; a novel privacy measure aimed at evaluating the resistance of social graphs to active attacks.  ...  (k, )-anonymity is based on a new problem in Graph Theory, the k-metric antidimension defined as follows.  ...  It also introduces the k-metric antidimension as the basis for the privacy measure (k, )-anonymity.  ... 
doi:10.1016/j.ins.2015.08.048 fatcat:sxt7ebz5lfdchj75dog5sjiumy

K-metric antidimension of some generalized Petersen graphs

Jozef Kratica, Vera Kovacevic-Vujcic, Mirjana Cangalovic
2019 Filomat  
Recently introduced k-metric antidimension graph invariant is used to define a new measure for resistance of social graphs.  ...  In this paper we have found and proved the k-metric antidimension for generalized Petersen graphs GP(n, 1) and GP(n, 2).  ...  For some graphs with special structures it would be interesting to investigate the privacy measure based on the k-metric antidimension.  ... 
doi:10.2298/fil1913085k fatcat:5c6jtclbjbddbagw4sub24f5au

k , l -Anonymity in Wheel-Related Social Graphs Measured on the Base of k -Metric Antidimension

Jiang-Hua Tang, Tahira Noreen, Muhammad Salman, Masood Ur Rehman, Jia-Bao Liu, Ali Ahmad
2021 Journal of Mathematics  
By determining their k -metric antidimension, we prove that each social graph of these families is the maximum degree metric antidimensional, where the degree of a vertex is the number of vertices linked  ...  In this regard, a novel privacy measure, called the k , l -anonymity, is used since the last few years on the base of k -metric antidimension of G in which l is the maximum number of attacker nodes defining  ...  Trujillo-Rasua and Yero defined, studied in detail, and promoted the idea of k-metric antidimension, which provides a basis for the privacy measure (k, l)-anonymity [7] . ey defined this privacy measure  ... 
doi:10.1155/2021/8038253 fatcat:xphufcovfvakjgrlvrsxdh3ag4

A Review of Several Privacy Violation Measures for Large Networks under Active Attacks [chapter]

Tanima Chatterjee, Nasim Mobasheri, Bhaskar DasGupta
2020 Ethics, Laws, and Policies for Privacy, Security, and Liability [Working Title]  
measure for social networks.  ...  However, since such anonymization processes may not always succeed, an important research goal is to quantify and measure how much privacy a given social network can achieve.  ...  Yero for useful discussions. This research was partially supported by NSF grants IIS-1160995 and IIS-1814931.  ... 
doi:10.5772/intechopen.90909 fatcat:is77dhuxvbbn7msphcajwlgxdy

Counteracting Active Attacks in Social Network Graphs [chapter]

Sjouke Mauw, Rolando Trujillo-Rasua, Bochuan Xuan
2016 Lecture Notes in Computer Science  
Active attackers can affect the structure of the social network graphs actively and use structural information, as a passive attacker does, to re-identify a user in a social graph.  ...  Consequently, social graphs, which express the relations between the actors in a social network, ought to be sanitized or anonymized before being published.  ...  Related work Most privacy notions for social graphs are based on k-anonymity [9] , which was originally proposed as a privacy measure for microdata.  ... 
doi:10.1007/978-3-319-41483-6_17 fatcat:3aepovfzkjdexoobb5s3s5zhcu

Anonymising social graphs in the presence of active attackers

Sjouke Mauw, Yunior Ramírez-Cruz, Rolando Trujillo-Rasua
2018 Transactions on Data Privacy  
To that end, we introduce a class of perturbation methods based on edge additions that transform a (1, 1)-anonymous graph into a graph satisfying (k, )-anonymity for some k > 1 or some > 1.  ...  This article addresses the challenge of publishing social graphs with proven privacy guarantees.  ...  Ergo, the 1-metric antidimension of this graph is 1.  ... 
dblp:journals/tdp/MauwRT18 fatcat:4xif4e2pxfdazd4lysrwsdfsqi

Rethinking (k,ℓ)-anonymity in social graphs: (k,ℓ)-adjacency anonymity and (k,ℓ)-(adjacency) anonymous transformations [article]

Sjouke Mauw, Yunior Ramírez-Cruz, Rolando Trujillo-Rasua
2017 arXiv   pre-print
The new privacy property is in turn the basis for a new type of graph perturbation: (k,ℓ)-adjacency anonymous transformations.  ...  This paper treats the privacy-preserving publication of social graphs in the presence of active adversaries, that is, adversaries with the ability to introduce sybil nodes in the graph prior to publication  ...  The notion of (k, ℓ)-anonymity was introduced in [11] as a measure of the resistance of a social graph to active attacks.  ... 
arXiv:1704.07078v1 fatcat:ydvxxxr44vfi7fg2u3bg3ymgke

On analyzing and evaluating privacy measures for social networks under active attack

Bhaskar DasGupta, Nasim Mobasheri, Ismael G. Yero
2018 Information Sciences  
Widespread usage of complex interconnected social networks such as Facebook, Twitter and LinkedIn in modern internet era has also unfortunately opened the door for privacy violation of users of such networks  ...  Our theoretical result indicates that the network manager responsible for prevention of privacy violation must be very careful in designing the network if its topology does not contain a cycle.  ...  Acknowledgements We thank the anonymous reviewers for their helpful comments. B.D. and N.M. thankfully acknowledges partially support from NSF grant IIS-1160995.  ... 
doi:10.1016/j.ins.2018.09.023 fatcat:i7uvkffuevb5pkvhn2l5myehdu

On the Computational Complexities of Three Privacy Measures for Large Networks Under Active Attack [article]

Tanima Chatterjee, Bhaskar DasGupta, Nasim Mobasheri, Venkatkumar Srinivasan, Ismael G. Yero
2016 arXiv   pre-print
In this paper, we formalize three such privacy measures for large networks and provide non-trivial theoretical computational complexity results for computing these measures.  ...  such a network by analyzing the network and deliberately using such privacy violations for deleterious purposes.  ...  This privacy measure relies on a graph parameter called the k-metric anti-dimension.  ... 
arXiv:1607.01438v1 fatcat:k7ah6zwls5e2hfiwsnjlpqt3we

Conditional adjacency anonymity in social graphs under active attacks

Sjouke Mauw, Yunior Ramírez-Cruz, Rolando Trujillo-Rasua
2018 Knowledge and Information Systems  
In doing so, social graphs need to be anonymised to resist various privacy attacks.  ...  We achieve this goal by introducing (k, G, )-adjacency anonymity: a privacy property based on (k, )-anonymity that alleviates the computational burden suffered by anonymisation algorithms based on (k,  ...  [4] , who showed that the k-metric antidimension problem used in (k, )anonymity is NP-Hard.  ... 
doi:10.1007/s10115-018-1283-x fatcat:6f5mdiscsvbljcgzjg4fizneoq

Two Novel Network Measures and Their Applications with a Case Study on ADHD for Human Brain Networks

Tanima Chatterjee
results and tools can be used for practical applications in both biological and social networks.  ...  In this thesis, I would be describing my work on the use of two novel network measures that use graph theoretic and computational tools to analyze heterogeneous complex networks and show how these algorithmic  ...  This leads us to our third problem: Problem 3 (k = -metric antidimension or Adim =k ).  ... 
doi:10.25417/uic.15261984 fatcat:ds64oaguqrexxl6cmgjxr6qxnm