Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited information. In contrast, real data often contain entities with different types or/and from different sources, which are comprehensive and can be better modeled by multiple networks. To take advantage of rich information in multiple networks and make better inferences on entities, in this study, we propose random walk on multiple networks, RWM. RWM is flexible and supports both multiplex networks and general multiple networks, which may form many-to-many node mappings between networks. RWM sends a random walker on each network to obtain the local proximity (i.e., node visiting probabilities) w.r.t. the starting nodes. Walkers with similar visiting probabilities reinforce each other. We theoretically analyze the convergence properties of RWM. Two approximation methods with theoretical performance guarantees are proposed for efficient computation. We apply RWM in link prediction, network embedding, and local community detection. Comprehensive experiments conducted on both synthetic and real-world datasets demonstrate the effectiveness and efficiency of RWM.

翻译：随机游走是一种探索网络结构的基础算法，可用于局部社区检测和网络嵌入等任务。现有随机游走方法基于信息有限的单一网络，而真实数据通常包含不同类型或/和不同来源的实体，这些实体具有综合性特征，更适合用多重网络建模。为充分利用多重网络的丰富信息并改善对实体的推断，本研究提出多重网络上的随机游走算法RWM。RWM具有灵活性，既支持多路复用网络，也支持可能形成网络间多对多节点映射的通用多重网络。RWM在每个网络上发送随机游走器以获得相对于起始节点的局部邻近性（即节点访问概率），具有相似访问概率的游走器会相互强化。我们从理论上分析了RWM的收敛特性，并提出了两种具有理论性能保证的近似计算方法。我们将RWM应用于链接预测、网络嵌入和局部社区检测任务。在合成数据集和真实数据集上进行的大量实验证明了RWM的有效性和高效性。