  Interaction networks, consisting of agents linked by their interactions, are
ubiquitous across many disciplines of modern science. Many methods of analysis
of interaction networks have been proposed, mainly concentrating on node degree
distribution or aiming to discover clusters of agents that are very strongly
connected between themselves. These methods are principally based on
graph-theory or machine learning.
  We present a mathematically simple formalism for modelling context-specific
information propagation in interaction networks based on random walks. The
context is provided by selection of sources and destinations of information and
by use of potential functions that direct the flow towards the destinations. We
also use the concept of dissipation to model the aging of information as it
diffuses from its source.
  Using examples from yeast protein-protein interaction networks and some of
the histone acetyltransferases involved in control of transcription, we
demonstrate the utility of the concepts and the mathematical constructs
introduced in this paper.
