Vector representations obtained from word embedding are the source of many groundbreaking advances in natural language processing. They yield word representations that are capable of capturing semantics and analogies of words within a text corpus. This study is an investigation in an attempt to elicit a vector representation of relationships between pairs of word vectors. We use six pooling strategies to represent vector relationships. Different types of clustering models are applied to analyze which one correctly groups relationship types. Subtraction pooling coupled with a centroid based clustering mechanism shows better performances in our experimental setup. This work aims to provide directions for a word embedding based unsupervised method to identify the nature of a relationship represented by a pair of words.