Real-world networks typically display a complex structure that is hard to explain by a single model. A common approach is to partition the edges of the network into disjoint simpler structures. An important property in this context is locality—incident vertices usually have many common neighbors. This allows to classify edges into two groups, based on the number of the common neighbors of their incident vertices. Formally, this is captured by the common-neighbors (CN) metric, which forms the basis of many metrics for detecting outlier edges. Such outliers can be interpreted as noise or as a substructure. We aim to understand how useful the metric is, and empirically analyze several scenarios. We randomly insert outlier edges into real-world and generated graphs with high locality, and measure the metric accuracy for partitioning the combined edges. In addition, we use the metric to decompose real-world networks, and measure properties of the partitions. Our results show that the CN metric is a very good classifier that can reliably detect noise up to extreme levels (83% noisy edges). We also provide mathematically rigorous analyses on special random-graph models. Last, we find the CN metric consistently decomposes real-world networks into two graphs with very different structures.