Working for Influence: Effect of Network Density and Modularity on Diffusion in Networks

The problem of finding the most influential individuals, or the largest spreaders, in networks has been shown to be NP-complete even for simple spreading models, though approximable by a simple greedy algorithm. Yet, even the greedy algorithm relies on stochastic simulations that can be quite time consuming and intractable for large networks. Recently developed heuristics are fast and work well in practice but are limited to certain network models, spreading goals, or sampled networks. In this work, instead of devising a new spread optimization method, we re-examine the problem by analyzing the global structural properties of the underlying network as indicators of spread trends. Specifically, our investigations use density of a network as an indicator of: (a) when it is necessary to employ a sophisticated yet computationally expensive method? or (b) when even a random set of spread initiators perform as well as the best in expectation for maximizing the spread in the network? and (c) why certain heuristics like high degree as indicator of high spread work for certain networks and not for others. We show that for network densities above and below a certain threshold, the difference between the best and expected spread is negligible. In between the two extremes, the networks exhibit marked differences between the best and expected spread. This region, rich with non-trivial and complicated structures, requires further work to devise efficient techniques for finding best spreaders.