Routledge Dictionary of Language and Linguistics
Two-place relation R for which, regarding any three objects x, y, z, it is the case that 
This is the case, for example, for some kinship terms: if it is the case that Philip is the brother of Jacob and Jacob is the brother of Caroline, then it is also true that Philip is the brother of Caroline.
On the other hand, the relation ‘is a friend of is not transitive: x is a friend of z may be false, if x is a friend of y and y is a friend of z is true. A relation is intransitive if there are no three objects x, y, z, for which it is true that 
for example, it cannot be the case that x is the father of y, y is the father of z and x is the father of z.
References
formal logic, set theory
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