Related papers: Any Graph is a Mapper Graph
Recent advancements in graph representation learning have led to the emergence of condensed encodings that capture the main properties of a graph. However, even though these abstract representations are powerful for downstream tasks, they…
We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc…
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…
In this paper, we propose algorithms for the graph isomorphism (GI) problem that are based on the eigendecompositions of the adjacency matrices. The eigenvalues of isomorphic graphs are identical. However, two graphs $ G_A $ and $ G_B $ can…
This paper describes a new approach to the problem of generating the class of all geodetic graphs homeomorphic to a given geodetic one. An algorithmic procedure is elaborated to carry out a systematic finding of such a class of graphs. As a…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
We investigate a special case of the Induced Subgraph Isomorphism problem, where both input graphs are interval graphs. We show the NP-hardness of this problem, and we prove fixed-parameter tractability of the problem with non-standard…
In the field of complex networks and graph theory, new results are typically tested on graphs generated by a variety of algorithms such as the Erd\H{o}s-R\'{e}nyi model or the Barab\'{a}si-Albert model. Unfortunately, most graph generating…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of…
Graph neural network (GNN) is a popular tool to learn the lower-dimensional representation of a graph. It facilitates the applicability of machine learning tasks on graphs by incorporating domain-specific features. There are various options…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
The Mapper algorithm is a fundamental tool in exploratory topological data analysis for identifying connectivity and topological clustering in data. Derived from the nerve construction, Mapper graphs can contain additional information about…
It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…
All graphs considered are simple and undirected. The Inverse Eigenvalue Problem of a Graph $G$ (IEP-G) aims to find all possible spectra for matrices whose $(i,j)-$entry, for $i\neq j$, is nonzero precisely when $i$ is adjacent to $j$. A…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
Graphs are widely used to model complicated data semantics in many application domains. In this paper, two novel and efficient algorithms Fast-ON and Fast-P are proposed for solving the subgraph isomorphism problem. The two algorithms are…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
Lane-level traversal of (almost) arbitrary input paths is a common problem in the mapping industry. This paper considers the problem of generating \emph{feasible} and maximally convenient lane-level path traversals. The presented approach…