Abstract
Counting (
p
,
q
)-bicliques in bipartite graphs is essential for uncovering dense substructures and higher-order patterns. However, releasing biclique counts can reveal private connections of users. To address this, we study (
p
,
q
)-biclique counting under edge local differential privacy, where each vertex protects its one-hop neighbor relationships from an untrusted data curator. The Naive algorithm applies randomized responses to the adjacency matrix and produces an overly dense graph where (
p
,
q
)-biclique structures are disrupted, resulting in highly biased estimates. To produce unbiased estimates, we propose a one-round algorithm that enumerates all motifs with
p
upper and
q
lower vertices, which leverages motif transformation probabilities to correct for perturbation-induced bias. To improve data utility and reduce the impact of Laplace noise, we propose a novel Multi-round Common Neighbor (MRCN) algorithm. MRCN estimates the number of common neighbors for each
p
-tuple (or
q
-tuple) and applies moment-based correction to recover unbiased (
p
,
q
)-biclique counts. Notably, MRCN avoids explicit enumeration of all (
p
,
q
)-motifs, offering better scalability for general
p
and
q
. We further boost performance with variance-reduction techniques such as multi-center optimization and refined noisy graph construction, and enhance scalability through layer-based pruning and vertex sampling. Extensive experiments on real-world datasets confirm the effectiveness and efficiency of our approaches.
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