Probabilistic spreading of recommendations in social networks

In this paper, we study how the recommendation of a product spreads across a social network assuming all members of the network recommend the product to their neighbors in a probabilistic manner. To do so, we consider a social network which is typically characterized by a scale-free network obeying power-law degree distribution. We take a layer-by-layer approach where nodes are labeled by how far they are from the origin node. Starting with the layer-1 nodes, we first compute the probability when the recommendation propagates outward from origin node considering the out-degree distribution. Then, we compute the probabilities when recommendations are made from nodes that are farther from the origin to nodes that are closer to the origin. Also, using the concept of clustering coefficient, we consider the recommendation probabilities within the same layer. Combining different possibilities, we are able to find the total effect. In order to demonstrate how recommendation spreads, we use Facebook data from SNAP and show how many nodes receive the recommendation in each layer and what the effect of the location of a node is with respect to the origin node.