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Single linkage can result in long stringy clusters and chaining while complete linkage tends to make highly compact clusters 1. One disadvantage of complete linkage clustering is that it behaves badly when outliers are present 2. This is not a problem with single linkage.

In Average linkage clustering, the distance between two clusters is defined as the average of distances between all pairs of objects, where each pair is made up of one object from each group. D(r,s) = Trs / ( Nr Ns) Where Trs is the sum of all pairwise distances between cluster r and cluster s.

Complete-linkage (farthest neighbor) is where distance is measured between the farthest pair of observations in two clusters. This method usually produces tighter clusters than single-linkage, but these tight clusters can end up very close together.

A hierarchical clustering is often represented as a dendrogram (from Manning et al. 1999). In complete-link (or complete linkage) hierarchical clustering, we merge in each step the two clusters whose merger has the smallest diameter (or: the two clusters with the smallest maximum pairwise distance).

Complete linkage clustering is the distance between the most distant elements in each cluster. By comparison, single linkage measures similarity of the most similar pair. Which one you use (single linkage or complete linkage) depends on your data and what you want to achieve by clustering.

The complete linkage method is a hierarchical classification method where the distance between two classes is defined as the greatest distance that could be obtained if we select one element from each class and measure the distance between these elements.

In statistics, single-linkage clustering is one of several methods of hierarchical clustering. It is based on grouping clusters in bottom-up fashion (agglomerative clustering), at each step combining two clusters that contain the closest pair of elements not yet belonging to the same cluster as each other.