DISTANCE-DEGREE BASED ASSESSMENT OF (k, )-ANONYMITY IN EVEN REGULAR CIRCULANT NETWORKS AND ITS APPLICATIONS TO TOPOLOGICAL INDICES

DISTANCE-DEGREE BASED ASSESSMENT OF (k, )-ANONYMITY IN EVEN REGULAR CIRCULANT NETWORKS AND ITS APPLICATIONS TO TOPOLOGICAL INDICES

Tahira Noreen, Muhammad Salman

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Abstract

This paper presents a graph-theoretic framework to evaluate (k, ℓ)-anonymity in circulant-like social networks using the concept of distance-degree. The (k, ℓ)-anonymity model protects against active attacks by ensuring that at least k nodes remain indistinguishable based on their distance profiles. We identify k-antimetric generators and compute k-metric antidimensions using τ -distance neighborhoods and their degrees, forming equivalence classes that define privacy levels. Exact conditions for optimal anonymity in even regular circulant networks Cn(1, 2, . . . , q) are established. Moreover, the framework extends naturally to compute key topological indices: the Wiener index and the distance eccentric connectivity index. Our findings reveal that even a single well-chosen node can provide strong anonymity guarantees in these networks.

Keywords

(k, ℓ)-anonymity; k-antimetric generator (k-AMG); k-metric antidimension; distance-degree; circulant networks; structural privacy; Wiener index; distance eccentric connectivity index.