Information spreading among nodes of directed random networks by means ofthe linear preferential attachment (PA) schemes and the well-known SPREAD algorithm isconsidered. The novelty of the paper is that schemes of the linear preferential attachment proposedin Wan et al. (2020) for the network evolution are also used here for the information spreading.The SPREAD algorithm proposed for undirected random graphs is adapted to directed graphs.Moreover, we deal with non-homogeneous directed networks consisting of nodes whose in-and out-degrees have different power law distributions that is realistic for practice and we findcommunities in a network that spread the information faster. We compare the minimum numberof evolution stepsK∗required for the preferential attachment schemes and the well-knownalgorithm SPREAD to spread a message among a fixed number of nodes. The evolution of thenetwork in time starts from a seed set of nodes. We study the impact of the seed network andparameters of the preferential attachment onK∗for simulated graphs. Real temporal graphs arealso investigated in the same way. The PA may be a better spreader than the SPREAD algorithm.This is valid for the sets of the PA parameters with dominating proportions of created new edgesfrom existing nodes to newly appending ones or between the existing nodes only. It is shown bothfor simulated and real graphs that the communities with the smallest tail indices of the out-degreesand PageRanks may spread the message faster than other communities
