Related papers: An In-Depth Analysis of Stochastic Kronecker Graph…

The analysis of massive graphs is now becoming a very important part of science and industrial research. This has led to the construction of a large variety of graph models, each with their own advantages. The Stochastic Kronecker Graph…

Large-scale analysis of the distributions of the network graphs observed in naturally-occurring phenomena has revealed that the degrees of such graphs follow a power-law or lognormal distribution. Seshadhri, Pinar, and Kolda (J. ACM, 2013)…

The stochastic Kronecker Graph model can generate large random graph that closely resembles many real world networks. For example, the output graph has a heavy-tailed degree distribution, has a (low) diameter that effectively remains…

Recently Stochastic Kronecker Graph (SKG), a network generation model, and vertex-centric BSP, a graph processing framework like Pregel, have attracted much attention in the network analysis community. Unfortunately the two are not very…

Generative models for graphs are increasingly becoming a popular tool for researchers to generate realistic approximations of graphs. While in the past, focus was on generating graphs which follow general laws, such as the power law for…

Researchers developing implementations of distributed graph analytic algorithms require graph generators that yield graphs sharing the challenging characteristics of real-world graphs (small-world, scale-free, heavy-tailed degree…

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…

Growing interest in modeling large, complex networks has spurred significant research into generative graph models. Kronecker-style models (SKG and R-MAT) are often used due to their scalability and ability to mimic key properties of…

The stochastic Kronecker graph model introduced by Leskovec et al. is a random graph with vertex set $\mathbb Z_2^n$, where two vertices $u$ and $v$ are connected with probability…

Representation learning over graph structure data has been widely studied due to its wide application prospects. However, previous methods mainly focus on static graphs while many real-world graphs evolve over time. Modeling such evolution…

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and…

Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to…

Graph learning, or network inference, is a prominent problem in graph signal processing (GSP). GSP generalizes the Fourier transform to non-Euclidean domains, and graph learning is pivotal to applying GSP when these domains are unknown.…

Random graph models are playing an increasingly important role in various fields ranging from social networks, telecommunication systems, to physiologic and biological networks. Within this landscape, the random Kronecker graph model,…

Massive power-law graphs drive many fields: metagenomics, brain mapping, Internet-of-things, cybersecurity, and sparse machine learning. The development of novel algorithms and systems to process these data requires the design, generation,…

The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase…

Graph learning algorithms have attained state-of-the-art performance on many graph analysis tasks such as node classification, link prediction, and clustering. It has, however, become hard to track the field's burgeoning progress. One…

Obtaining real-world network datasets is often challenging because of privacy, security, and computational constraints. In the absence of such datasets, graph generative models become essential tools for creating synthetic datasets. In this…

Stochastic Kronecker graphs are a model for complex networks where each edge is present independently according the Kronecker (tensor) product of a fixed matrix k-by-k matrix P with entries in [0,1]. We develop a novel correspondence…

Graph models have long been used in lieu of real data which can be expensive and hard to come by. A common class of models constructs a matrix of probabilities, and samples an adjacency matrix by flipping a weighted coin for each entry.…