  PageRank has been widely used to measure the authority or the influence of a
user in social networks. However, conventional PageRank only makes use of
edge-based relations, which represent first-order relations between two
connected nodes. It ignores higher-order relations that may exist between
nodes. In this paper, we propose a novel framework, motif-based PageRank (MPR),
to incorporate higher-order relations into the conventional PageRank
computation. Motifs are subgraphs consisting of a small number of nodes. We use
motifs to capture higher-order relations between nodes in a network and
introduce two methods, one linear and one non-linear, to combine PageRank with
higher-order relations. We conduct extensive experiments on three real-world
networks, namely, DBLP, Epinions, and Ciao. We study different types of motifs,
including 3-node simple and anchor motifs, 4-node and 5-node motifs. Besides
using single motif, we also run MPR with ensemble of multiple motifs. We also
design a learning task to evaluate the abilities of authority prediction with
motif-based features. All experimental results demonstrate that MPR can
significantly improve the performance of user ranking in social networks
compared to the baseline methods.
