Cycle index of uncertain random graph

Chen, Lin; Peng, Jin; Rao, Congjun; Rosyida, Isnaini

doi:10.3233/jifs-17373

Cited by 13 publications

(6 citation statements)

References 48 publications

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“…As deleting a vertex would deleting all edges incident to it, κ is smaller than κ for most graphs. For example, let H = (V , E) be the graph, where V = {1, 2, 3, 4, 5} and E = {(1, 2), (2,3), (1,3), (3,4), (4,5), (3,5)}. Then κ(H ) = 1 as H − {3} is disconnected.…”

Section: A Notations Of Graph Theorymentioning

confidence: 99%

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On the Vertex-Connectivity of an Uncertain Random Graph

Gao

2020

IEEE Access

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In many practical problems, randomness and uncertainty simultaneously appear in one complex system or network. When graph theory is applied to these problems, these complex systems or networks are usually represented by uncertain random graphs, in which some edges exist with degrees in probability measure, and some other edges exist with degrees in uncertain measure. In this paper, we focus on the connectivity of uncertain random graphs with respect to vertices. We propose the concepts of k-vertexconnectivity index and the connectivity of an uncertain random graph. The former is the chance measure that an uncertain random graph is k-vertex-connected, and the latter is an uncertain random variable, which characterizes the connectivity of the uncertain random graph with respect to vertices. We discuss some properties of these concepts. Methods and formulas are also presented for calculating the k-vertexconnectivity index, and the distribution and expected value of the connectivity of an uncertain random graph.

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Section: A Notations Of Graph Theorymentioning

confidence: 99%

“…They also discussed the matching index of an uncertain random graph in 2018 [36]. In 2018, Chen et al [5] discussed the cycle index of an uncertain random graph. For more knowledge about chance theory and uncertain random graphs, the readers may refer to [15], [16], [23]- [25], [26], [30], [31], [38].…”

Section: Introductionmentioning

confidence: 99%

On the Vertex-Connectivity of an Uncertain Random Graph

Gao

2020

IEEE Access

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“…Graph theory has gained recognition in research in more recent years. Graph theory in human studies often presents vertex covering problems which are classified under determinacy environmental problems in which all the edges and vertices can be completely determined [17]. One area of classical graph theory application is in social networks [18] [19].…”

Section: Social Network Theory and Analysismentioning

confidence: 99%

The Complexities of Employee and Institutional Interactions for Human Capital Development: Evidence from Banking Network of Ghana

Dankyi¹,

Kong²,

Peprah³

et al. 2020

OALib

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The paper focused on the human capital development capacity of complex interactive institutional networks. Network principles were adopted to seek the underlying conditions that determine the human capital development of institutions as well as its capacity to sustain personnel development within competitively dense networks. The research focused on existing management structures hinged on the assumption that it influenced policy development, implementation, and worker engagements intending to increase institutional performance within the competitive space. Using some core attributes, a network was developed to capture the interaction between employees within an institution as well as their comparative impact on the general banking system of a developing economy. Using specific network measures, we deduced the institutional network was efficient in human capital development, and also efficiency in competitive networks is inversely proportional to density. Multinational Banks have higher potentials of human capital development in a highly competitive industry compared to indigenous banks. Again connectivity dynamics affect human capital development in financial networks in developing countries.

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“…In 2016, the Euler index of an uncertain random graph was discussed by Zhang, Peng and Li [33]. In 2018, the cycle index of an uncertain random graph was discussed by Chen et al [3]. In 2020, Li and Zhang discussed the edge-connectivity of uncertain random graph, and the vertex-connectivity of uncertain random graph was investigated by Li and Gao. In this paper, we will propose the model of uncertain random digraph, and discuss the shortest path problem.…”

Section: Introductionmentioning

confidence: 99%

On the Shortest Path Problem of Uncertain Random Digraphs

Zhang

2021

Preprint

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In the field of graph theory, the shortest path problem is one of the most significant problems. However, since varieties of indeterminated factors appear in complex networks, determining of the shortest path from one vertex to another in complex networks may be a lot more complicated than the cases in deterministic networks. To illustrate this problem, the model of uncertain random digraph will be proposed via chance theory, in which some arcs exist with degrees in probability measure and others exist with degrees in uncertain measure. The main focus of this paper is to investigate the main properties of the shortest path in uncetain random digraph. Methods and algorithms are designed to calculate the distribution of shortest path more efficiently. Besides, some numerical examples are presented to show the efficiency of these methods and algorithms.

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Cycle index of uncertain random graph

Cited by 13 publications

References 48 publications

On the Vertex-Connectivity of an Uncertain Random Graph

On the Vertex-Connectivity of an Uncertain Random Graph

The Complexities of Employee and Institutional Interactions for Human Capital Development: Evidence from Banking Network of Ghana

On the Shortest Path Problem of Uncertain Random Digraphs

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