Biblio

Triangle count is a critical parameter in mining relationships among people in social networks. However, directly publishing the findings obtained from triangle counts may bring potential privacy concern, which raises great challenges and opportunities for privacy-preserving triangle counting. In this paper, we choose to use differential privacy to protect triangle counting for large scale graphs. To reduce the large sensitivity caused in large graphs, we propose a novel graph projection method that can be used to obtain an upper bound for sensitivity in different distributions. In particular, we publish the triangle counts satisfying the node-differential privacy with two kinds of histograms: the triangle count distribution and the cumulative distribution. Moreover, we extend the research on privacy preserving triangle counting to one of its applications, the local clustering coefficient. Experimental results show that the cumulative distribution can fit the real statistical information better, and our proposed mechanism has achieved better accuracy for triangle counts while maintaining the requirement of differential privacy.

Triangles are the most basic non-trivial subgraphs. Triangle counting is used in a number of different applications, including social network mining, cyber security, and spam detection. In general, triangle counting algorithms are readily parallelizable, but when implemented in distributed, shared-memory, their performance is poor due to high communication, imbalance of work, and the difficulty of exploiting locality available in shared memory. In this paper, we discuss four different (but related) triangle counting algorithms and how their performance can be improved in distributed, shared-memory by reducing in-node load imbalance, improving cache utilization, minimizing network overhead, and minimizing algorithmic work. We generalize the four different triangle counting algorithms into a common framework and show that for all four algorithms the in-node load imbalance can be minimized while utilizing caches by partitioning work into blocks of vertices, the network overhead can be minimized by aggregation of blocks of work, and algorithm work can be reduced by partitioning vertex neighbors by degree. We experimentally evaluate the weak and the strong scaling performance of the proposed algorithms with two types of synthetic graph inputs and three real-world graph inputs. We also compare the performance of our implementations with the distributed, shared-memory triangle counting algorithms available in PowerGraph-GraphLab and show that our proposed algorithms outperform those algorithms, both in terms of space and time.