Kolmogorov Basic Graphs and Their Application in Network Complexity Analysis

Throughout the years, measuring the complexity of networks and graphs has been of great interest to scientists. The Kolmogorov complexity is known as one of the most important tools to measure the complexity of an object. We formalized a method to calculate an upper bound for the Kolmogorov complexity of graphs and networks. Firstly, the most simple graphs possible, those with O(1) Kolmogorov complexity, were identified. These graphs were then used to develop a method to estimate the complexity of a given graph. The proposed method utilizes the simple structures within a graph to capture its non-randomness. This method is able to capture features that make a network closer to the more non-random end of the spectrum. The resulting algorithm takes a graph as an input and outputs an upper bound to its Kolmogorov complexity. This could be applicable in, for example evaluating the performances of graph compression methods.

Computation of Topological Indices of NEPS of Graphs

The inspection of the networks and graphs through structural properties is a broad research topic with developing significance. One of the methods in analyzing structural properties is obtaining quantitative measures that encode data of the whole network by a real quantity. A large quantity of graph-associated numerical invariants has been used to examine the whole structure of networks. In this analysis, degree-related topological indices have a significant place in nanotechnology and theoretical chemistry. Thereby, the computation of indices is one of the successful branches of research. The noncomplete extended p -sum NEPS of graphs is a famous general graph product. In this paper, we investigated the exact formulas of general zeroth-order Randić, Randić, and the first multiplicative Zagreb indices for NEPS of graphs.

Mathematical methods in technological design

On the basis of the analysis of technological design problems there is shown a possibility for the formalization of initial stages of metal-working production technological preparation at the expense of algebraic structures of discrete mathematics, methods and algorithms of the probability theory, the theory of networks and graphs, the theory of fuzzy sets.

Integrated development of carrying capacities of the Baikal-Amur Mainline and Trans-Siberian Railway

The paper considers actual technical and technological problems in the development of the Eastern polygon of the Russian railway network. The purpose of the study is to develop a methodology and software tools that ensure the search for effective solutions for given resource and logistical constraints. Methods of simulation modeling, distribution of flows on networks and graphs are used. The result of the study is a hybrid set of model calculations.

Além do portão de desembarque: uma análise da conectividade dos aeroportos portugueses e suas implicações sobre os fluxos migratórios / Beyond the boarding gate: an analysis of the Portuguese airports and their implications on migration flows

<p>Este artigo tem como objetivo discutir a posição estratégica de Portugal no mapa migratório da Europa, a partir dos fluxos aéreos coletados entre os aeroportos do país, outros aeroportos da União Europeia e países de língua portuguesa. Baseia-se na concepção de redes e grafos para elaborar um retrato da conectividade aérea, através da análise de dados de voos de um dia de semana típico. Mediante análise comparativa da conectividade aérea de Portugal e de outros aeroportos europeus, desperta para a vulnerabilidade de aeroportos e cidades situados em nós aéreos estratégicos, bem como para a necessidade de estudos sobre as redes de tráfego aéreo, paralelamente às redes sociais de migrantes.</p><p><strong> </strong></p><p><strong>Palavras-chave:</strong> Portugal, migrações, aeroportos, redes.<strong></strong></p><p><strong><em><span style="text-decoration: underline;"> </span></em></strong></p><p><strong>Abstract </strong></p><p>This paper aims at discussing the strategic position of Portugal on the migratory map of Europe from the perspective of the connections among its airports and other airports located in the European Union and in Portuguese-speaking countries. The approach relies on the concepts of networks and graphs to draw a picture of air connectivity from flight data collected on a typical weekday. The comparative analysis of air connectivity in Portugal, other airports in Europe and airports of Portuguese-speaking countries intends to shed a light on the vulnerability of airports and cities that represent nodal points from the perspective of air flows, as well as on the need for further studies that focus on aerial networks and social networks simultaneously. </p><p><strong> </strong></p><p><strong>Keywords:</strong> Portugal, migrations, airports, networks.</p>