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Local dependency in networks

100%

Kudělka M., Zehnalová Š., Horák Z., Krömer P., Snášel V.

International Journal of Applied Mathematics and Computer Science

2015

tom 25

nr 2

281-293

Many real world data and processes have a network structure and can usefully be represented as graphs. Network analysis focuses on the relations among the nodes exploring the properties of each network. We introduce a method for measuring the strength of the relationship between two nodes of a network and for their ranking. This method is applicable to all kinds of networks, including directed and weighted networks. The approach extracts dependency relations among the network's nodes from the structure in local surroundings of individual nodes. For the tasks we deal with in this article, the key technical parameter is locality. Since only the surroundings of the examined nodes are used in computations, there is no need to analyze the entire network. This allows the application of our approach in the area of large-scale networks. We present several experiments using small networks as well as large-scale artificial and real world networks. The results of the experiments show high effectiveness due to the locality of our approach and also high quality node ranking comparable to PageRank.

Physicist’s approach to public transportation networks: between data processing and statistical physics

100%

Korduba Y., Holovatch Y., de Regt R.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2019

tom 73

nr 2

In this paper we aim to demonstrate how physical perspective enriches statistical analysis when dealing with a complex system of many interacting agents of non-physical origin. To this end, we discuss analysis of urban public transportation networks viewed as complex systems. In such studies, a multi-disciplinary approach is applied by integrating methods in both data processing and statistical physics to investigate the correlation between public transportation network topological features and their operational stability. These studies incorporate concepts of coarse graining and clusterization, universality and scaling, stability and percolation behavior, diffusion and fractal analysis.

Embeddings of hamiltonian paths in faulty k-ary 2-cubes

100%

Wang S., Zhang S.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 1

47-61

It is well known that the k-ary n-cube has been one of the most efficient interconnection networks for distributed-memory parallel systems. A k-ary n-cube is bipartite if and only if k is even. Let (X,Y) be a bipartition of a k-ary 2-cube (even integer k ≥ 4). In this paper, we prove that for any two healthy vertices u ∈ X, v ∈ Y, there exists a hamiltonian path from u to v in the faulty k-ary 2-cube with one faulty vertex in each part.

Ograniczanie wyników

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Discussiones Mathematicae Graph Theory

1 International Journal of Applied Mathematics and Computer Science

1 Holovatch Y.

1 Horák Z.

1 Korduba Y.

1 Krömer P.

1 Kudělka M.

1 Snášel V.

1 Wang S.

1 Zehnalová Š.

1 Zhang S.

1 de Regt R.

1 2019

1 2015

1 2012

Wyniki wyszukiwania

Local dependency in networks

Physicist’s approach to public transportation networks: between data processing and statistical physics

Embeddings of hamiltonian paths in faulty k-ary 2-cubes