  A heavy path in a weighted graph represents a notion of connectivity and
ordering that goes beyond two nodes. The heaviest path of length l in the
graph, simply means a sequence of nodes with edges between them, such that the
sum of edge weights is maximum among all paths of length l. It is trivial to
state the heaviest edge in the graph is the heaviest path of length 1, that
represents a heavy connection between (any) two existing nodes. This can be
generalized in many different ways for more than two nodes, one of which is
finding the heavy weight paths in the graph. In an influence network, this
represents a highway for spreading information from a node to one of its
indirect neighbors at distance l. Moreover, a heavy path implies an ordering of
nodes. For instance, we can discover which ordering of songs (tourist spots) on
a playlist (travel itinerary) is more pleasant to a user or a group of users
who enjoy all songs (tourist spots) on the playlist (itinerary). This can also
serve as a hard optimization problem, maximizing different types of quantities
of a path such as score, flow, probability or surprise, defined as edge weight.
Therefore, if one can solve the Heavy Path Problem (HPP) efficiently, they can
as well use HPP for modeling and reduce other complex problems to it.
