Related papers: Motif Estimation via Subgraph Sampling: The Fourth…
Dynamic networks, a.k.a. graph streams, consist of a set of vertices and a collection of timestamped interaction events (i.e., temporal edges) between vertices. Temporal motifs are defined as classes of (small) isomorphic induced subgraphs…
Applied researchers often construct a network from a random sample of nodes in order to infer properties of the parent network. Two of the most widely used sampling schemes are subgraph sampling, where we sample each vertex independently…
Assessing homophily in large-scale networks is central to understanding structural regularities in graphs, and thus inform the choice of models (such as graph neural networks) adopted to learn from network data. Evaluation of smoothness…
Exploring statistics of locally connected subgraph patterns (also known as network motifs) has helped researchers better understand the structure and function of biological and online social networks (OSNs). Nowadays the massive size of…
The mining of pattern subgraphs, known as motifs, is a core task in the field of graph mining. Edges in real-world networks often have timestamps, so there is a need for temporal motif mining. A temporal motif is a richer structure that…
We introduce a new method for finding network motifs: interesting or informative subgraph patterns in a network. Subgraphs are motifs when their frequency in the data is high compared to the expected frequency under a null model. To compute…
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 identification and counting of small graph patterns, called network motifs, is a fundamental primitive in the analysis of networks, with application in various domains, from social networks to neuroscience. Several techniques have been…
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…
Pattern counting in graphs is fundamental to network science tasks, and there are many scalable methods for approximating counts of small patterns, often called motifs, in large graphs. However, modern graph datasets now contain richer…
Given a graph sequence $\{G_n\}_{n\ge1}$ and a simple connected subgraph $H$, we denote by $T(H,G_n)$ the number of monochromatic copies of $H$ in a uniformly random vertex coloring of $G_n$ with $c \ge 2$ colors. In this article, we prove…
Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a…
We investigate the distribution of monochromatic subgraph counts in random vertex $2$-colorings of large graphs. We give sufficient conditions for the asymptotic normality of these counts and demonstrate their essential necessity…
Network moments--rescaled counts of motifs such as stars and triangles--are fundamental summaries of network structure, widely used in goodness-of-fit testing, model selection, and network comparison. While the univariate distribution of a…
Counting the frequency of small subgraphs is a fundamental technique in network analysis across various domains, most notably in bioinformatics and social networks. The special case of triangle counting has received much attention. Getting…
While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the…
We address the problem of understanding the variable abundance of 3-node and 4-node subgraphs (motifs) in complex networks from a dynamical point of view. As a criterion in the determination of the functional significance of a n-node…
Transcription networks, and other directed networks can be characterized by some topological observables such as for example subgraph occurrence (network motifs). In order to perform such kind of analysis, it is necessary to be able to…
Characterizing motif (i.e., locally connected subgraph patterns) statistics is important for understanding complex networks such as online social networks and communication networks. Previous work made the strong assumption that the graph…
We consider a statistical model for the problem of finding subgraphs with specified topology in an otherwise random graph. This task plays an important role in the analysis of social and biological networks. In these types of networks,…