Detection of human relationships from their interactions on social media is a challenging problem with a wide range of applications in different areas like targeted marketing, cyber-crime, fraud, defense, planning, human resource, to name a few. All previous work in this area has only dealt with the most basic types of relationships. The proposed approach goes beyond the previous work to efficiently handle the hierarchy of social relationships. This paper introduces a novel technique named Quantifiable Social Relationship (QSR) analysis for quantifying social relationships to analyze relationships between agents from their textual conversations. QSR uses cross-disciplinary techniques from computational linguistics and cognitive psychology to identify relationships. QSR utilizes sentiment and behavioral styles displayed in the conversations for mapping them onto level II relationship categories. Then, for identifying the level III relationship categories, QSR uses level II relationships, sentiments, interactions, and word embeddings as key features. QSR employs natural language processing techniques for feature engineering and state-of-the-art embeddings generated by word2vec, global vectors (glove), and bidirectional encoder representations from transformers (bert). QSR combines the intrinsic conversational features with word embeddings for classifying relationships. QSR achieves an accuracy of up to 89% for classifying relationship subtypes. The evaluation shows that QSR can accurately identify the hierarchical relationships between agents by extracting intrinsic and extrinsic features from textual conversations between agents.