Related papers: Same Stats, Different Graphs (Graph Statistics and…

We study the minimum cut problem in the presence of uncertainty and show how to apply a novel robust optimization approach, which aims to exploit the similarity in subsequent graph measurements or similar graph instances, without posing any…

We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…

A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…

Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in…

Three new graph invariants are introduced which may be measured from a quantum graph state and form examples of a framework under which other graph invariants can be constructed. Each invariant is based on distinguishing a different number…

We investigate the fundamental statistical features of tagged (or annotated) networks having a rich variety of attributes associated with their nodes. Tags (attributes, annotations, properties, features, etc.) provide essential information…

Feature generation is an open topic of investigation in graph machine learning. In this paper, we study the use of graph homomorphism density features as a scalable alternative to homomorphism numbers which retain similar theoretical…

Exploring small connected and induced subgraph patterns (CIS patterns, or graphlets) has recently attracted considerable attention. Despite recent efforts on computing the number of instances a specific graphlet appears in a large graph…

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…

Query answering routinely employs knowledge graphs to assist the user in the search process. Given a knowledge graph that represents entities and relationships among them, one aims at complementing the search with intuitive but effective…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. These optimal graphs, many of which are newly…

A fundamental problem on graph-structured data is that of quantifying similarity between graphs. Graph kernels are an established technique for such tasks; in particular, those based on random walks and return probabilities have proven to…

In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…

Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…

The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…

Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies. This…

Which one is better between two representative graph summarization models with and without edge weights? From web graphs to online social networks, large graphs are everywhere. Graph summarization, which is an effective graph compression…

Through legislation and technical advances users gain more control over how their data is processed, and they expect online services to respect their privacy choices and preferences. However, data may be processed for many different…

We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at…