Mining Triadic Closure Patterns in Social Networks

ABSTRACT A closed triad is a group of three people who are connected with each other. It is the most basic unit for studying group phenomena in social networks. In this paper, we study how closed triads are formed in dynamic networks. More specifically, given three persons, what are the fundamental factors that trigger the formation of triadic closure? There are various factors that may influence the formation of a relationship between persons. Can we design a unified model to predict the formation of triadic closure? Employing a large microblogging network as the source in our study, we formally define the problem and conduct a systematic investigation. The study uncovers how user demographics and network topology influence the process of triadic closure. We also present a probabilistic graphical model to predict whether three persons will form a closed triad in dynamic networks. The experimental results on the microblogging data demonstrate the efficiency of our proposed model for the prediction of triadic closure formation

Motifs in Temporal Networks

Networks are a fundamental tool for modeling complex systems in a variety of domains including social and communication networks as well as biology and neuroscience. Small subgraph patterns in networks, called network motifs, are crucial to understanding the structure and function of these systems. However, the role of network motifs in temporal networks, which contain many timestamped links between the nodes, is not yet well understood. Here we develop a notion of a temporal network motif as an elementary unit of temporal networks and provide a general methodology for counting such motifs. We define temporal network motifs as induced subgraphs on sequences of temporal edges, design fast algorithms for counting temporal motifs, and prove their runtime complexity. Our fast algorithms achieve up to 56.5x speedup compared to a baseline method. Furthermore, we use our algorithms to count temporal motifs in a variety of networks. Results show that networks from different domains have significantly different motif counts, whereas networks from the same domain tend to have similar motif counts. We also find that different motifs occur at different time scales, which provides further insights into structure and function of temporal networks

Understanding Negative Sampling in Graph Representation Learning

Graph representation learning has been extensively studied in recent years. Despite its potential in generating continuous embeddings for various networks, both the effectiveness and efficiency to infer high-quality representations toward large corpus of nodes are still challenging. Sampling is a critical point to achieve the performance goals. Prior arts usually focus on sampling positive node pairs, while the strategy for negative sampling is left insufficiently explored. To bridge the gap, we systematically analyze the role of negative sampling from the perspectives of both objective and risk, theoretically demonstrating that negative sampling is as important as positive sampling in determining the optimization objective and the resulted variance. To the best of our knowledge, we are the first to derive the theory and quantify that the negative sampling distribution should be positively but sub-linearly correlated to their positive sampling distribution. With the guidance of the theory, we propose MCNS, approximating the positive distribution with self-contrast approximation and accelerating negative sampling by Metropolis-Hastings. We evaluate our method on 5 datasets that cover extensive downstream graph learning tasks, including link prediction, node classification and personalized recommendation, on a total of 19 experimental settings. These relatively comprehensive experimental results demonstrate its robustness and superiorities.Comment: KDD 202

Predicting triadic closure in networks using communicability distance functions

We propose a communication-driven mechanism for predicting triadic closure in complex networks. It is mathematically formulated on the basis of communicability distance functions that account for the quality of communication between nodes in the network. We study $25$ real-world networks and show that the proposed method predicts correctly $20\%$ of triadic closures in these networks, in contrast to the $7.6\%$ predicted by a random mechanism. We also show that the communication-driven method outperforms the random mechanism in explaining the clustering coefficient, average path length, and average communicability. The new method also displays some interesting features with regards to optimizing communication in networks