adjacency matrix

简明释义

邻接矩阵;

英英释义

例句

1.In machine learning, the adjacency matrix 邻接矩阵 can be used for graph-based algorithms.

在机器学习中，邻接矩阵 adjacency matrix 可用于基于图的算法。

2.We can represent the connections of the social network using an adjacency matrix 邻接矩阵.

我们可以使用 邻接矩阵 adjacency matrix 表示社交网络的连接。

3.To determine if two nodes are connected, you can check the corresponding values in the adjacency matrix 邻接矩阵.

要确定两个节点是否连接，可以检查相应的 邻接矩阵 adjacency matrix 中的值。

4.In graph theory, an adjacency matrix 邻接矩阵 is used to represent a finite graph.

在图论中，邻接矩阵 adjacency matrix 用于表示有限图。

5.The adjacency matrix 邻接矩阵 for a directed graph is not symmetric.

有向图的 邻接矩阵 adjacency matrix 不是对称的。

作文

In the realm of computer science and graph theory, understanding the concept of an adjacency matrix is crucial for various applications, including network analysis, social network modeling, and even in algorithms for pathfinding. An adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. More specifically, if there is an edge connecting vertex i to vertex j, the element in the ith row and jth column of the adjacency matrix is marked with a 1; otherwise, it is marked with a 0. This simple yet powerful representation allows for efficient computations and easy visualization of graphs.To illustrate how an adjacency matrix works, let’s consider a simple undirected graph that consists of four vertices: A, B, C, and D. If we have edges connecting A to B, A to C, and B to D, the adjacency matrix for this graph would look like this: A B C D A 0 1 1 0 B 1 0 0 1 C 1 0 0 0 D 0 1 0 0In this matrix, the rows and columns correspond to the vertices of the graph. The presence of a '1' in the matrix indicates a direct connection between the vertices, while '0' indicates no direct connection. For example, looking at the first row, we see that vertex A is connected to vertices B and C (as indicated by the 1s), but not to vertex D (indicated by the 0).The adjacency matrix is particularly useful when it comes to performing operations on graphs. For instance, one can easily determine the degree of a vertex by summing the entries in its corresponding row or column. Moreover, matrix operations can be employed to discover paths within the graph. By raising the adjacency matrix to a power, one can find the number of paths of a given length between any two vertices. This property is leveraged in various algorithms, such as those used for finding the shortest path or detecting cycles in a graph.Another important aspect of the adjacency matrix is its scalability. While it is efficient for representing dense graphs where the number of edges is close to the maximum possible, it can become inefficient for sparse graphs with relatively few edges. In such cases, alternative representations, such as adjacency lists, may be more suitable. Nevertheless, the adjacency matrix remains a fundamental concept in graph theory due to its simplicity and effectiveness in many scenarios.In conclusion, the adjacency matrix serves as a vital tool for representing graphs in computer science. Its ability to succinctly capture the relationships between vertices enables various analytical methods and algorithms to be applied effectively. As technology continues to advance and the complexity of networks increases, mastering the use of an adjacency matrix will undoubtedly remain a valuable skill for computer scientists and data analysts alike. Understanding this concept not only enhances one's knowledge of graph theory but also equips individuals with the necessary tools to tackle real-world problems involving networks and connections.

在计算机科学和图论的领域中，理解邻接矩阵的概念对于各种应用至关重要，包括网络分析、社交网络建模，甚至是路径寻找算法。邻接矩阵是用来表示有限图的一个方阵。矩阵的元素指示图中一对顶点是否相邻。更具体地说，如果存在一条连接顶点i和顶点j的边，则邻接矩阵中第i行第j列的元素标记为1；否则，标记为0。这种简单而强大的表示法允许高效的计算和图形的直观可视化。为了说明邻接矩阵的工作原理，让我们考虑一个由四个顶点组成的简单无向图：A、B、C和D。如果我们有边连接A到B、A到C，以及B到D，那么该图的邻接矩阵将如下所示： A B C D A 0 1 1 0 B 1 0 0 1 C 1 0 0 0 D 0 1 0 0在这个矩阵中，行和列对应于图的顶点。矩阵中的'1'表示顶点之间存在直接连接，而'0'表示没有直接连接。例如，从第一行可以看出，顶点A与顶点B和C相连（由1表示），但与顶点D不相连（由0表示）。邻接矩阵在对图进行操作时特别有用。例如，可以通过对其对应行或列的条目求和来轻松确定一个顶点的度。此外，可以利用矩阵运算来发现图中的路径。通过将邻接矩阵提升到某个幂，可以找到任意两个顶点之间给定长度路径的数量。这一特性被用于各种算法，例如用于寻找最短路径或检测图中的循环。邻接矩阵的另一个重要方面是其可扩展性。虽然它在表示密集图时效率很高，但当图中边的数量相对较少时，它可能变得低效。在这种情况下，邻接表等替代表示法可能更为合适。然而，邻接矩阵由于其简单性和在许多场景中的有效性，仍然是图论的基本概念。总之，邻接矩阵作为计算机科学中表示图的重要工具，其简洁地捕捉顶点之间关系的能力，使各种分析方法和算法得以有效应用。随着技术的不断进步和网络复杂性的增加，掌握使用邻接矩阵无疑将成为计算机科学家和数据分析师的一项宝贵技能。理解这一概念不仅增强了人们对图论的认识，也为个人提供了应对涉及网络和连接的现实问题所需的工具。