Connectivity Determination Algorithm for Complex Directed Networks

IF 6.7 2区计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY

IEEE Transactions on Network Science and Engineering Pub Date : 2025-03-11 DOI:10.1109/TNSE.2025.3549777

Zhiyi Zhong;Lin Lin;Zhihan Jiang;Xin Yuan;Edith C.H. Ngai;James Lam;Ka-Wai Kwok

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引用次数: 0

Abstract

Connectivity characterizes the ability of information transmission in systems modeled by complex networks. It is essential to develop an efficient connectivity determination algorithm with low time complexity and minimal storage requirements. To fulfill this need, a connectivity determination algorithm is designed by incorporating Tarjan's algorithm to identify strongly connected components and leveraging a depth-first search idea to traverse the reachability. This algorithm can ascertain strong connectivity, unilateral connectivity, and weak connectivity of complex directed networks. Besides, the accessibility matrix of complex directed networks is computed and visualized through an interface. As this algorithm relies on only two depth-first searches to accomplish connectivity determination tasks, its computational complexity does not exceed

$O(n^{2})$

, where

$n$

denotes the number of network nodes. Experiments carried out on some specific networks reveal that the probability of network connections decreases with the increasing number of nodes in directed injective graphs, while in Erdős–Rényi graphs, the likelihood of connections increases as the number of nodes increases. Finally, a comparative example and an application example are provided to demonstrate the effectiveness of the algorithm program.

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复杂有向网络连通性判定算法

在由复杂网络建模的系统中，连通性表征了信息传输的能力。开发一种具有低时间复杂度和最小存储需求的高效连通性确定算法至关重要。为了满足这一需求，通过结合Tarjan的算法来识别强连接组件，并利用深度优先搜索思想来遍历可达性，设计了连接确定算法。该算法可以确定复杂有向网络的强连通性、单边连通性和弱连通性。此外，通过接口计算并可视化了复杂有向网络的可达性矩阵。由于该算法仅依赖于两次深度优先搜索来完成连通性确定任务，因此其计算复杂度不超过$O(n^{2})$，其中$n$表示网络节点数。在一些特定网络上进行的实验表明，在有向内射图中，网络连接的概率随着节点数量的增加而降低，而在Erdős-Rényi图中，网络连接的可能性随着节点数量的增加而增加。最后给出了一个比较算例和应用实例，验证了算法程序的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Network Science and Engineering Engineering-Control and Systems Engineering

CiteScore

12.60

自引率

9.10%

发文量

393

期刊介绍： The proposed journal, called the IEEE Transactions on Network Science and Engineering (TNSE), is committed to timely publishing of peer-reviewed technical articles that deal with the theory and applications of network science and the interconnections among the elements in a system that form a network. In particular, the IEEE Transactions on Network Science and Engineering publishes articles on understanding, prediction, and control of structures and behaviors of networks at the fundamental level. The types of networks covered include physical or engineered networks, information networks, biological networks, semantic networks, economic networks, social networks, and ecological networks. Aimed at discovering common principles that govern network structures, network functionalities and behaviors of networks, the journal seeks articles on understanding, prediction, and control of structures and behaviors of networks. Another trans-disciplinary focus of the IEEE Transactions on Network Science and Engineering is the interactions between and co-evolution of different genres of networks.