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Spectral embedding of graphs uses the top k non-trivial eigenvectors of the random walk matrix to embed the graph into R^k. The primary use of this embedding has been for practical spectral clustering algorithms [SM00,NJW02]. Recently,…
Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…
In dense Erd\H{o}s-R\'enyi random graphs, we are interested in the events where large numbers of a given subgraph occur. The mean behavior of subgraph counts is known, and only recently were the related large deviations results discovered.…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
Graph sampling via crawling has been actively considered as a generic and important tool for collecting uniform node samples so as to consistently estimate and uncover various characteristics of complex networks. The so-called simple random…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
Sampling is a widely used graph reduction technique to accelerate graph computations and simplify graph visualizations. By comprehensively analyzing the literature on graph sampling, we assume that existing algorithms cannot effectively…
Personalized PageRank (PPR) has enormous applications, such as link prediction and recommendation systems for social networks, which often require the fully PPR to be known. Besides, most of real-life graphs are edge-weighted, e.g., the…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…
Tree graphs are routinely used in statistics. When estimating a Bayesian model with a tree component, sampling the posterior remains a core difficulty. Existing Markov chain Monte Carlo methods tend to rely on local moves, often leading to…
Network embedding has been widely used in social recommendation and network analysis, such as recommendation systems and anomaly detection with graphs. However, most of previous approaches cannot handle large graphs efficiently, due to that…
Graph pattern matching algorithms to handle million-scale dynamic graphs are widely used in many applications such as social network analytics and suspicious transaction detections from financial networks. On the other hand, the computation…
Graphs are useful structures that can model several important real-world problems. Recently, learning graphs have drawn considerable attention, leading to the proposal of new methods for learning these data structures. One of these studies…
Are users of an online social network interested equally in all connections in the network? If not, how can we obtain a summary of the network personalized to specific users? Can we use the summary for approximate query answering? As…
In this paper we introduce a novel polynomial-time algorithm to compute graph invariants based on the modified random walk idea on graphs. However not proved to be a full graph invariant by now, our method gives the right answer for the…
A hypergraph is a generalization of a graph that arises naturally when attribute-sharing among entities is considered. Compared to graphs, hypergraphs have the distinct advantage that they contain explicit communities and are more…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
There are a number of existing studies analysing the convergence behaviour of graph neural networks on large random graphs. Unfortunately, the majority of these studies do not model correlations between node features, which would naturally…