Directed graphs and networks that have a small scale, high density, and a heavy tailed distribution of edge weights are interesting research objects due to these specified characteristics. A prominent example of such networks is the World Trade Network of export-import flows between countries, whose density exceeds 90 %. When analyzing a network, researchers typically rely on basic characteristics traditionally used in graph theory and network analysis. This paper proposes an approach based on combining the “friendship paradox”, used to assess the local significance of network participants, with the disparity filter, applied to discard weak ties based on statistical significance. The obtained results and their substantive interpretation allow for a deeper understanding of the complex structure hidden behind the small dimensionality of such networks.