Related papers: Quantifying Network Similarity using Graph Cumulan…
In this article, we revisit and expand our prior work on graph similarity. As with our earlier work, we focus on a view of similarity which does not require node correspondence between graphs under comparison. Our work is suited to the…
Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse…
Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…
Counts of small subgraphs, or graphlet counts, are widely applicable to measure graph similarity. Computing graphlet counts can be computationally expensive and may pose obstacles in network analysis. We study the role of cliques in…
In many applications concerning statistical graphical models the data originate from several subpopulations that share similarities but have also significant differences. This raises the question of how to estimate several graphical models…
We consider that a network is an observation, and a collection of observed networks forms a sample. In this setting, we provide methods to test whether all observations in a network sample are drawn from a specified model. We achieve this…
In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the…
A wide range of tasks in network analysis, such as clustering network populations or identifying anomalies in temporal graph streams, require a measure of the similarity between two graphs. To provide a meaningful data summary for…
How can researchers test for heterogeneity in the local structure of a network? In this paper, we present a framework that utilizes random sampling to give subgraphs which are then used in a goodness of fit test to test for heterogeneity.…
Assessing generative models is not an easy task. Generative models should synthesize graphs which are not replicates of real networks but show topological features similar to real graphs. We introduce an approach for assessing graph…
Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This paper presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples. It can…
Graph isomorphism is a problem for which there is no known polynomial-time solution. Nevertheless, assessing (dis)similarity between two or more networks is a key task in many areas, such as image recognition, biology, chemistry, computer…
A wide range of models have been proposed for Graph Generative Models, necessitating effective methods to evaluate their quality. So far, most techniques use either traditional metrics based on subgraph counting, or the representations of…
Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original…
The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…
Graphs are naturally used to describe the structures of various real-world systems in biology, society, computer science etc., where subgraphs or motifs as basic blocks play an important role in function expression and information…
We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…