Related papers: Graph Theory in the Classification of Information …
Graph Machine Learning (Graph ML) has witnessed substantial advancements in recent years. With their remarkable ability to process graph-structured data, Graph ML techniques have been extensively utilized across diverse applications,…
The graph isomorphism problem has a long history in mathematics and computer science, with applications in computational chemistry and biology, and it is believed to be neither solvable in polynomial time nor NP-complete. E. Luks proposed…
Moving an autonomous agent through an unknown environment is one of the crucial problems for robotics and network analysis. Therefore, it received a lot of attention in the last decades and was analyzed in many different settings. The graph…
A circulant graph H is defined on the set of vertices V=\left\{ 1,\ldots,n\right\} and edges E=\left\{ \left(i,j\right):\left|i-j\right|\equiv s\left(\textrm{mod}n\right),s\in S\right\} , where S\subseteq\left\{…
Graph pattern matching is a routine process for a wide variety of applications such as social network analysis. It is typically defined in terms of subgraph isomorphism which is NP-Complete. To lower its complexity, many extensions of graph…
Temporal Graph Neural Networks, a new and trending area of machine learning, suffers from a lack of formal analysis. In this paper, information theory is used as the primary tool to provide a framework for the analysis of temporal GNNs. For…
In the context of understanding the nature of the risk transformation process of the financial system we propose an iterative risk-trading game between several agents who build their trading strategies based on a general utility setting.…
The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum of given functions evaluated at the subgraph degrees. Here we study this problem by replacing degree sequences, via suitable nonlinear…
It's important to design polynomial time algorithms to test if two graphs are isomorphic at least for some special classes of graphs. An approach to this was presented by Eugene M. Luks(1981) in the work \textit{Isomorphism of Graphs of…
The clique-width is a measure of complexity of decomposing graphs into certain tree-like structures. The class of graphs with bounded clique-width contains bounded tree-width graphs. We give a polynomial time graph isomorphism algorithm for…
Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
The paper addresses the graph classification problem and introduces a modification of the lazy associative classification method to efficiently handle intersections of graphs. Graph intersections are approximated with all common subgraphs…
Document structure analysis, such as zone segmentation and table recognition, is a complex problem in document processing and is an active area of research. The recent success of deep learning in solving various computer vision and machine…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
In this article we demonstrate how graph theory can be used to identify those stations in the London underground network which have the greatest influence on the functionality of the traffic, and proceed, in an innovative way, to assess the…
Coordination graph is a promising approach to model agent collaboration in multi-agent reinforcement learning. It conducts a graph-based value factorization and induces explicit coordination among agents to complete complicated tasks.…
We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of…
The work deals with the risk assessment theory. An unitary risk algorithm is elaborated. The algorithm is based on parallel curves. The basic curve of risk is a hyperbolic curve, obtained as a multiplication between the probability of…
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…