Uncovering hidden dependency in weighted networks via information entropy

Abstract

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.

arXiv comment20 pages, 15 figures

References in corpus (21)

• Assortative mixing in networks
• The Building Blocks of Economic Complexity
• Mixing patterns in networks
• The Product Space Conditions the Development of Nations
• Critical phenomena in complex networks
• Extracting the multiscale backbone of complex weighted networks
• Scale-free networks are rare
• Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes
• Scale-free Networks Well Done
• The effectiveness of backward contact tracing in networks
• Higher-Order Aggregate Networks in the Analysis of Temporal Networks: Path structures and centralities
• Googling Social Interactions: Web Search Engine Based Social Network Construction
• Statistical physics of complex information dynamics
• Phase transition in the recoverability of network history
• Intrinsic degree-correlations in static model of scale-free networks
• Evolutionary Games on Isothermal Graphs
• Modeling the dynamics of dissent
• Early onset of structural inequality in the formation of collaborative knowledge, Wikipedia
• Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time
• Giant component in a configuration-model power-law graph with a variable number of links
• Random Walks on Complex Networks

Cited by in corpus (2)

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