Discovering communities in complex networks is essential in performing analyses, such as dynamics of political fragmentation and echo chambers in social networks. In this work, we study the problem of quantifying the significance of edges in a complex network, and propose a significantly improved version of the Link Entropy method. Using Louvain, Leiden and Walktrap methods, our proposal detects the number of communities in each iteration on discovering the communities. Running experiments on various benchmark networks, we show that our proposed method outperforms the Link Entropy method in quantifying edge significance. Considering also the computational complexities and possible defects, we conclude that Leiden or Louvain algorithms are the best choice for community number detection in quantifying edge significance. We also discuss designing a new algorithm for not only discovering the number of communities, but also computing the community membership uncertainties.

Through online political communications, fragmented groups appear around ideological lines, which might form echo chambers if the communications within like-minded groups are dominant over the communications among different-minded groups, potentially contributing to political polarization and extremism. The antidote is the interactions between individuals who constitute social bridges between different minded groups. Hence, exploring the significance of connections between the individuals of a network is a center of attraction especially for the global connectivity and diffusion in networks. Based on the divergence of probability distributions of pairs of nodes, Link Entropy (LE) is a recently proposed method outperforming the others in quantifying edge significance. In this work, considering that the adjacent nodes of the two nodes of an edge are also in charge in determining its significance, we propose the Deep Link Entropy (DLE) method for a more precise quantification through taking into account the uncertainty distributions of the adjacent nodes as well. We show experimentally that DLE significantly outperforms LE especially in large-scale complex network with several groups or communities. We believe our method contributes to not only online political communications but a wide range of fields from biology to quantum networks, where edge significance has an operational meaning.

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