As the complexity of a system increases, in practical application of graph theory, different types of uncertainty are frequently encountered. In an uncertain graph, whether two vertices of the graph are joined cannot be completely determined. Within the framework of uncertainty theory, the concept of Euler index of uncertain graph is proposed. It also gives a method to calculate Euler index of ...

This paper considers the Euler tour of an uncertain random graph, in which some edges exist with some degrees in uncertain measure and others exist with some degrees in probability measure. The concept of Euler index of an uncertain random graph is proposed first, and then a method to calculate the Euler index of an uncertain random graph is given. In addition, some properties of the Euler inde...

The connectivity of graph is a basic concept of graph theory. Since originated in seven bridges problem by Euler in 1736, the main study of graph theory unfolds on the assumption that the graph is connected. In classic graph theory, the edges and the vertices are all deterministic, and connectivity of the graph can be easily verified. However, in practical application, non-deterministic factors...

With the increasingly development of system complexity, there is a variety of indeterminacy in the practical applications of graph theory. In this paper, the uncertainty theory is applied to study the regularity of the uncertain graph. Based on the uncertainty theory, the concept of regularity index of uncertain graph and its calculation method are raised with an illustration of the calculation...

ith the increasingly development of system complexity, there is a variety of uncertainties in the practical applications of graph theory. In this paper, the uncertainty theory is applied to study the regularity of the uncertain graph. Based on the uncertainty theory, the concept of regularity index of uncertain graph and its calculation method are raised with an illustration of the calculation ...

Data in several applications can be represented as an uncertain graph, whose edges are labeled with a probability of existence. Currently, most query and mining tasks on uncertain graphs are based on Monte-Carlo sampling, which is rather time consuming for the large uncertain graphs commonly found in practice (e.g., social networks). To overcome the high cost, in this doctoral work we propose t...