In terminology, relationship is a state of connection or association between two or more individuals.  In the world of the personal, of work, and of the world at large, relationships between people are a decisive force.  In the scientific perspective, relationships are often quantified by their interaction components.
In sociological-psychology, a relationship is considered as a long interaction or function of a set of multitudes of microsecond interactions. An interaction between two individuals involves, at a minimum, individual A showing behavior X to individual B. Individual B may, in turn, respond with behavior Y. There may be a number of such repetitions of this sequence, involving behavior that is consistent or different, but an interaction is essentially limited in time.  A relationship, subsequently, involves a series of such interactions between individuals who know each other, such that each interaction is affected by preceding ones and usually by the expectation of future interactions. 
1. (a) Relationship (definition) – Dictionary.com
(b) Relationship (definition) – Merriam-Webster Collegiate Dictionary (2000).
2. Gilbert, Roberta, M. (1992). Extraordinary Relationships – a New Way of Thinking About Human Interactions, (pg. 3). New York: John Wiley & Sons.
3. Auhagen, Ann E. and Salish, Maria v. (1996). The Diversity of Human Relationships, (pg. 9). New York: Cambridge University Press.
4. (a) Bateson, G. (1979). Mind and Culture: a Necessary Unity. New York: Dutton.
(b) Rogers, L.E. and Millar, F.E. (1988). “Persuasion in Personal Relationships”, in S. Duck (Ed.), Handbook of Personal Relationships (pgs. 289-306). Chichester, England: Wiley.