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Community detection in social networks is a topic of central importance in modern graph mining, and the existence of overlapping communities has recently given rise to new interest in arc clustering. In this paper, we propose the notion of triangular random walk as a way to unveil arc-community structure in social graphs: a triangular walk is a random process that insists differently on arcs that close a triangle. We prove that triangular walks can be used effectively, by translating them into a standard weighted random walk on the line graph, our experiments show that the weights so defined are in fact very helpful in determining the similarity between arcs and yield high-quality clustering. Even if our technique gives a weighting scheme on the line graph and can be combined with any node-clustering method in the final phase, to make our approach more scalable we also propose an algorithm (ALP) that produces the clustering directly without the need to build the weighted line graph explicitly. Our experiments show that ALP, besides providing the largest accuracy, it is also the fastest and most scalable among all arc-clustering algorithms we are aware of.