As Personalized PageRank has been widely leveraged for ranking on a graph, the efficient computation of Personalized PageRank Vector (PPV) becomes a prominent issue. In this paper, we propose FastPPV, an approximate PPV computation algorithm that is incremental and accuracy-aware. Our approach hinges on a novel paradigm of scheduled approximation: the computation is partitioned and scheduled for processing in an "organized" way, such that we can gradually improve our PPV estimation in an incremental manner, and quantify the accuracy of our approximation at query time. Guided by this principle, we develop an efficient hub based realization, where we adopt the metric of hub-length to partition and schedule random walk tours so that the approximation error reduces exponentially over iterations. Furthermore, as tours are segmented by hubs, the shared substructures between different tours (around the same hub) can be reused to speed up query processing both within and across iterations. Finally, we evaluate FastPPV over two real-world graphs, and show that it not only significantly outperforms two state-of-the-art baselines in both online and offline phrases, but also scale well on larger graphs. In particular, we are able to achieve near-constant time online query processing irrespective of graph size.

Most existing community-related studies focus on detection, which aim to find the community membership for each user from user friendship links. However, membership alone, without a complete profile of what a community is and how it interacts with other communities, has limited applications. This motivates us to consider systematically profiling the communities and thereby developing useful community-level applications. In this paper, we for the first time formalize the concept of community profiling. With rich user information on the network, such as user published content and user diffusion links, we characterize a community in terms of both its internal content profile and external diffusion profile. The difficulty of community profiling is often underestimated. We novelly identify three unique challenges and propose a joint Community Profiling and Detection (CPD) model to address them accordingly. We also contribute a scalable inference algorithm, which scales linearly with the data size and it is easily parallelizable. We evaluate CPD on large-scale real-world data sets, and show that it is significantly better than the state-of-the-art baselines in various tasks.

Many real-world networks have a rich collection of objects. The semantics of these objects allows us to capture different classes of proximities, thus enabling an important task of semantic proximity search. As the core of semantic proximity search, we have to measure the proximity on a heterogeneous graph, whose nodes are various types of objects. Most of the existing methods rely on engineering features about the graph structure between two nodes to measure their proximity. With recent development on graph embedding, we see a good chance to avoid feature engineering for semantic proximity search. There is very little work on using graph embedding for semantic proximity search. We also observe that graph embedding methods typically focus on embedding nodes, which is an "indirect'' approach to learn the proximity. Thus, we introduce a new concept of proximity embedding, which directly embeds the network structure between two possibly distant nodes. We also design our proximity embedding, so as to flexibly support both symmetric and asymmetric proximities. Based on the proximity embedding, we can easily estimate the proximity score between two nodes and enable search on the graph. We evaluate our proximity embedding method on three real-world public data sets, and show it outperforms the state-of-the-art baselines.

Proximity search on heterogeneous graphs aims to measure the proximity between two nodes on a graph w.r.t. some semantic relation for ranking. Pioneer work often tries to measure such proximity by paths connecting the two nodes. However, paths as linear sequences have limited expressiveness for the complex network connections. In this paper, we explore a more expressive DAG (directed acyclic graph) data structure for modeling the connections between two nodes. Particularly, we are interested in learning a representation for the DAGs to encode the proximity between two nodes. We face two challenges to use DAGs, including how to efficiently generate DAGs and how to effectively learn DAG embedding for proximity search. We find distance-awareness as important for proximity search and the key to solve the above challenges. Thus we develop a novel Distance-aware DAG Embedding (D2AGE) model. We evaluate D2AGE on three benchmark data sets with six semantic relations, and we show that D2AGE outperforms the state-of-the-art baselines. We release the code on https://github.com/shuaiOKshuai.