  Interactions between elements, which are usually represented by networks,
have to delineate potentially unequal relationships in terms of their relative
importance or direction. The intrinsic unequal relationships of such kind,
however, are opaque or hidden in numerous real systems. For instance, when a
node in a network with limited interaction capacity spends its capacity to its
neighboring nodes, the allocation of the total amount of interactions to them
can be vastly diverse. Even if such potentially heterogeneous interactions
epitomized by weighted networks are observable, as a result of the
aforementioned ego-centric allocation of interactions, the relative importance
or dependency between two interacting nodes can only be implicitly accessible.
In this work, we precisely pinpoint such relative dependency by proposing the
framework to discover hidden dependent relations extracted from weighted
networks. For a given weighted network, we provide a systematic criterion to
select the most essential interactions for individual nodes based on the
concept of information entropy. The criterion is symbolized by assigning the
effective number of neighbors or the effective out-degree to each node, and the
resultant directed subnetwork decodes the hidden dependent relations by leaving
only the most essential directed interactions. We apply our methodology to two
time-stamped empirical network data, namely the international trade relations
between nations in the world trade web (WTW) and the network of people in the
historical record of Korea, Annals of the Joseon Dynasty (AJD). Based on the
data analysis, we discover that the properties of mutual dependency encoded in
the two systems are vastly different.
