In a modern contemporary business scenario, the organizations (Providers) and the stakeholders (e.g. Consumers) require recommendation or ranking systems that satisfy a variety of functional (features) and non-functional requirements (e.g. QoS) with varied preferences. The paper presents a novel graph model called \(M^{2}B\) graph that represents mutual requirements having varied preferences of providers and requester. The graph based mutual requirement matchmaking mechanism is explored which considers the multiple functional attributes (features or parameters) with preferences representing weights. The matchmaking mechanism adopts functional (pattern) matching, extended semantic matching and simple additive weighting (SAW) to rank the potential outcomes as recommendations to both the parties. We develop the proof of concept for the proposed recommendation mechanism called HIREASY which provides a platform for job seekers and recruiters to upload their requirements and preferences. We construct a multi-weighted bipartite graph for each candidate-employer requirement with varied preferences. Further, the weighted sum (score) of the potential matches is calculated and the ranking of mutual requirements for candidate-employer pair is generated. The experimental observations reveal that the proposed multi-weighted bipartite-graph model explores all relevant matches for the mutual requirements and ranks them based on the varied preferences of the mutual requirements.