Deep Link Entropy for Quantifying Edge Significance in Social Networks

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.

Bottleneck links, essential intermediaries, and competing paths of diffusion in networks

We investigate how information goods are priced and diffused over links in a network. A new equivalence relation between nodes captures the effects of network architecture and locations of sellers on the division of profits, and characterizes the topology of competing (and potentially overlapping) diffusion paths. Sellers indirectly appropriate profits over intermediation chains from buyers in their equivalence classes. Links within the same class constitute bottlenecks for information diffusion and confer monopoly power. Links that bridge distinct classes are redundant for diffusion and generate competition among sellers. In dense networks, competition limits the scope of indirect appropriability and intellectual property rights foster innovation.

Diffusion in networks and the virtue of burstiness

Whether an idea, information, or infection diffuses throughout a society depends not only on the structure of the network of interactions, but also on the timing of those interactions. People are not always available to interact with others, and people differ in the timing of when they are active. Some people are active for long periods and then inactive for long periods, while others switch more frequently from being active to inactive and back. We show that maximizing diffusion in classic contagion processes requires heterogeneous activity patterns across agents. In particular, maximizing diffusion comes from mixing two extreme types of people: those who are stationary for long periods of time, changing from active to inactive or back only infrequently, and others who alternate frequently between being active and inactive.