Related papers: Use of Eigenvector Centrality to Detect Graph Isom…
In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…
The eccentricity matrix of a simple connected graph is derived from its distance matrix by preserving the largest non-zero distance in each row and column, while the other entries are set to zero. This article examines the…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
The problem of node-similarity in networks has motivated a plethora of such measures between node-pairs, which make use of the underlying graph structure. However, higher-order relations cannot be losslessly captured by mere graphs and…
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
Graph hyperdimensional computing (HDC) has emerged as a promising paradigm for cognitive tasks, emulating brain-like computation with high-dimensional vectors known as hypervectors. While HDC offers robustness and efficiency on…
Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative perspective, modeling large networks as exchangeable graphs…
This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising…
Arrhythmias, detectable through electrocardiograms (ECGs), pose significant health risks, underscoring the need for accurate and efficient automated detection techniques. While recent advancements in graph-based methods have demonstrated…
A set $S$ of isometric paths of a graph $G$ is ``$v$-rooted'', where $v$ is a vertex of $G$, if $v$ is one of the endpoints of all the isometric paths in $S$. The isometric path complexity of a graph $G$, denoted by $ipco{G}$, is the…
This paper addresses the challenge of spectral analysis and structural investigation for graphs that are not distance-regular, where computing the spectrum using standard methods based on equitable and orbit partitions can be complex. Our…
In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some…
An $H$-graph is an intersection graph of connected subgraphs of a suitable subdivision of a fixed graph $H$. Many important classes of graphs, including interval graphs, circular-arc graphs, and chordal graphs, can be expressed as…
Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…
The network alignment (or graph matching) problem refers to recovering the node-to-node correspondence between two correlated networks. In this paper, we propose a network alignment algorithm which works without using a seed set of…
The graph isomorphism (GI) problem, which asks whether two graphs are structurally identical, occupies a unique position in computational complexity -- it is neither known to be solvable in polynomial time, nor proven to be NP-complete. We…
We consider heuristic algorithm for solving graph isomorphism problem. The algorithm based on a successive splitting of the eigenvalues of the matrices which are modifications (to positive defined) of graphs' adjacency matrices.…
To determine if two lists of numbers are the same set, we sort both lists and see if we get the same result. The sorted list is a canonical form for the equivalence relation of set equality. Other canonical forms arise in graph isomorphism…
Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…
Given two graphs $H_1$ and $H_2$, a graph $G$ is $(H_1,H_2)$-free if it contains no induced subgraph isomorphic to $H_1$ or $H_2$. Let $P_t$ be the path on $t$ vertices. A graph $G$ is $k$-vertex-critical if $G$ has chromatic number $k$ but…