Related papers: Conway's law, revised from a mathematical viewpoin…
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…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
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…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
This paper extends graphic statics by describing the forces and moments in any 3D rigid-jointed frame structure in terms of cell complexes using homology theory of algebraic topology. Graphic statics provides a highly geometric way to…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed graph $H$ as a minor to graphs excluding $H$ as a topological subgraph. We prove that for a fixed $H$, every graph excluding $H$ as a topological…
Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two…
In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of…
Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…
Graph convolution (GConv) is a widely used technique that has been demonstrated to be extremely effective for graph learning applications, most notably node categorization. On the other hand, many GConv-based models do not quantify the…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
Given graphs $X$ and $Y$, we define two conic feasibility programs which we show have a solution over the completely positive cone if and only if there exists a homomorphism from $X$ to $Y$. By varying the cone, we obtain similar…
Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon Sowa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given…