Temporal graph representation learning (T-GRL) aims to learn representations that model how graph edges evolve over time. While recent works on T-GRL have improved link prediction accuracy in temporal settings, their methods optimize a point-wise loss function independently over future links rather than optimize jointly over a candidate set per node. In applications where resources (e.g., attention) are allocated based on ranking links by likelihood, the use of a ranking loss is preferred. However it is not straightforward to develop a T-GRL method to optimize a ranking loss due to a tradeoff between model expressivity and scalability. In this work, we address these issues and propose a Temporal Graph network for Ranking (TGRank), which significantly improves performance for link prediction tasks by (i) optimizing a list-wise loss for improved ranking, and (ii) incorporating a labeling approach designed to allow for efficient inference over the candidate set jointly, while provably boosting expressivity. We extensively evaluate TGRank over six real networks. TGRank outperforms the state-of-the-art baselines on average by 14.21%↑ (transductive) and 16.25% ↑ (inductive) in ranking metrics while being more efficient (up-to 65 × speed-up) to make inference on large networks.

We consider the enumeration of dense substructures (maximal cliques) from an uncertain graph. For parameter 0 <; α <; 1, we define the notion of an a-maximal clique in an uncertain graph. We present matching upper and lower bounds on the number of a-maximal cliques possible within a (uncertain) graph. We present an algorithm to enumerate a-maximal cliques whose worst-case runtime is near-optimal, and an experimental evaluation showing the practical utility of the algorithm.

We consider the enumeration of maximal bipartite cliques (bicliques) from a large graph, a task central to many data mining problems arising in social network analysis and bioinformatics. We present novel parallel algorithms for the MapReduce framework, and an experimental evaluation using Hadoop MapReduce. Our algorithm is based on clustering the input graph into smaller subgraphs, followed by processing different subgraphs in parallel. Our algorithm uses two ideas that enable it to scale to large graphs: (1) the redundancy in work between different subgraph explorations is minimized through a careful pruning of the search space, and (2) the load on different reducers is balanced through a task assignment that is based on an appropriate total order among the vertices. We show theoretically that our algorithm is work optimal, i.e., it performs the same total work as its sequential counterpart. We present a detailed evaluation which shows that the algorithm scales to large graphs with millions of edges and tens of millions of maximal bicliques. To our knowledge, this is the first work on maximal biclique enumeration for graphs of this scale.

We consider mining dense substructures (maximal cliques) from an uncertain graph, which is a probability distribution on a set of deterministic graphs. For parameter 0 <; α <; 1, we consider the notion of an α-maximal clique in an uncertain graph. We present matching upper and lower bounds on the number of α-maximal cliques possible within a (uncertain) graph. We present an algorithm to enumerate α-maximal cliques whose worst-case runtime is near-optimal, and an experimental evaluation showing the practical utility of the algorithm.