complete graph

简明释义

完全图

英英释义

例句

1.In graph theory, a complete graph (完全图) is defined as a graph in which every pair of distinct vertices is connected by a unique edge.

在图论中，complete graph (完全图)被定义为一个图，其中每对不同的顶点都由一条独特的边连接。

2.In a network of five computers, the best way to ensure maximum connectivity is to use a complete graph (完全图).

在五台计算机的网络中，确保最大连接性的最佳方法是使用一个complete graph (完全图)。

3.The complete graph (完全图) on four vertices has six edges connecting every pair of vertices.

四个顶点的complete graph (完全图)有六条边连接每一对顶点。

4.To solve this problem efficiently, we can model it as a complete graph (完全图) and apply algorithms designed for such structures.

为了高效解决这个问题，我们可以将其建模为一个complete graph (完全图)，并应用针对这种结构设计的算法。

5.When modeling social networks, researchers often represent friendships as a complete graph (完全图) where everyone knows each other.

在建模社交网络时，研究人员通常将友谊表示为一个complete graph (完全图)，其中每个人都相互认识。

作文

In the field of graph theory, a complete graph is a type of graph in which every pair of distinct vertices is connected by a unique edge. This means that if there are 'n' vertices in a complete graph, there will be exactly n(n-1)/2 edges. For example, a complete graph with three vertices, denoted as K3, has three edges connecting each vertex to every other vertex. The concept of a complete graph is fundamental in various areas of mathematics and computer science, particularly in network design, where it represents a scenario where every node is directly connected to every other node.Understanding the properties of a complete graph can provide insights into more complex structures. For instance, it is known that a complete graph is always connected, meaning there is a path between any two vertices. This characteristic is crucial in applications such as communication networks where connectivity is essential. Furthermore, the presence of numerous edges in a complete graph implies that they have high redundancy, which can be advantageous in fault-tolerant systems.In practical scenarios, while a complete graph may not always be feasible due to cost or physical constraints, it serves as a useful theoretical model. For instance, in social network analysis, a complete graph can represent a situation where every individual knows every other individual, allowing researchers to study phenomena like information spread or group dynamics.Moreover, the concept of a complete graph extends beyond theoretical implications. In computer algorithms, the complete graph serves as a benchmark for testing the efficiency of various algorithms, particularly those related to pathfinding and optimization. For example, the traveling salesman problem, which seeks the shortest possible route visiting a set of cities and returning to the origin city, can be visualized using a complete graph. Each city represents a vertex, and the paths between them represent the edges.In conclusion, the complete graph is a vital structure in graph theory that illustrates the relationship between vertices and edges in a highly interconnected manner. Its applications span across various fields, including mathematics, computer science, and social sciences, making it an essential concept for anyone interested in understanding networks and their behaviors. By studying complete graphs, we gain valuable insights into connectivity, redundancy, and optimization, which are critical in our increasingly interconnected world.

在图论领域，完全图是一种图，其中每对不同的顶点之间都由一条唯一的边连接。这意味着如果在一个完全图中有'n'个顶点，那么将恰好有n(n-1)/2条边。例如，一个具有三个顶点的完全图，记作K3，具有三条边连接每个顶点与其他顶点。完全图的概念在数学和计算机科学的各个领域中都是基础，特别是在网络设计中，它代表了每个节点都直接连接到其他节点的情况。理解完全图的性质可以为更复杂的结构提供洞察。例如，已知完全图总是连通的，这意味着任何两个顶点之间都有路径。这一特性在通信网络等应用中至关重要，因为连通性是必不可少的。此外，完全图中边的数量众多意味着它们具有较高的冗余性，这在容错系统中是有利的。在实际场景中，虽然完全图由于成本或物理限制可能并不总是可行，但它作为一个有用的理论模型。例如，在社交网络分析中，完全图可以表示每个人都认识其他每个人的情况，从而使研究人员能够研究信息传播或群体动态等现象。此外，完全图的概念超越了理论意义。在计算机算法中，完全图作为测试各种算法效率的基准，特别是与路径寻找和优化相关的算法。例如，旅行推销员问题寻求访问一组城市并返回起始城市的最短路线，可以通过完全图进行可视化。每个城市代表一个顶点，而它们之间的路径则代表边。总之，完全图是图论中的一个重要结构，说明了顶点和边之间以高度相互连接的方式的关系。它的应用跨越多个领域，包括数学、计算机科学和社会科学，使其成为任何对理解网络及其行为感兴趣的人必不可少的概念。通过研究完全图，我们获得了关于连通性、冗余性和优化的宝贵见解，这在我们日益互联的世界中至关重要。