Related papers: Graph Comparison via the Non-backtracking Spectrum
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…
Graph embedding is a transformation of vertices of a graph into set of vectors. Good embeddings should capture the graph topology, vertex-to-vertex relationship, and other relevant information about graphs, subgraphs, and vertices. If these…
Graph theory has drawn a lot of attention in the field of Neuroscience during the last decade, mainly due to the abundance of tools that it provides to explore the interactions of elements in a complex network like the brain. The local and…
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.…
Causal discovery aims to recover graphs that represent causal relations among given variables from observations, and new methods are constantly being proposed. Increasingly, the community raises questions about how much progress is made,…
With the impressive growth of network models in practically every scientific and technological area, we are often faced with the need to compare graphs, i.e., to quantify their (dis)similarity using appropriate metrics. This is necessary,…
A non-backtracking walk on a graph, $H$, is a directed path of directed edges of $H$ such that no edge is the inverse of its preceding edge. Non-backtracking walks of a given length can be counted using the non-backtracking adjacency…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
Consider a random graph process where vertices are chosen from the interval $[0,1]$, and edges are chosen independently at random, but so that, for a given vertex $x$, the probability that there is an edge to a vertex $y$ decreases as the…
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…
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
The problem of measuring similarity of graphs and their nodes is important in a range of practical problems. There is a number of proposed measures, some of them being based on iterative calculation of similarity between two graphs and the…
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…
Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…
Graphs provide a natural way to represent data by encoding information about objects and the relationships between them. With the ever-increasing amount of data collected and generated, locating specific patterns of relationships between…
Much effort has been spent on characterizing the spectrum of the non-backtracking matrix of certain classes of graphs, with special emphasis on the leading eigenvalue or the second eigenvector. Much less attention has been paid to the…
Spectral methods offer a tractable, global framework for clustering in graphs via eigenvector computations on graph matrices. Hypergraph data, in which entities interact on edges of arbitrary size, poses challenges for matrix…
We estimate fair graphs from graph-stationary nodal observations such that connections are not biased with respect to sensitive attributes. Edges in real-world graphs often exhibit preferences for connecting certain pairs of groups. Biased…