Connectivity and hop count are two crucial attributes of dynamic wireless networks such as ad-hoc wireless networks (AHWNs). When the security issue is considered, establishing a secure multi-hop path in AHWNs is challenging because an intermediate node having a wireless link with previous nodes may not be secure to receive data from those nodes, and vice versa. In this paper, stochastic geometry graphs is used to model the AHWNs with eavesdroppers’ presence, then a simulation-based analysis method is proposed to investigate the characteristics of connectivity, hop count distribution, average hop count, and their relations in various scenarios. The proposed simulation-based analysis method consists of two algorithms. The first one finds all possible secure communication paths between two arbitrary legitimate users selected as source and destination and returns the shortest path’s hop count. This algorithm utilizes the random locations of legitimate users and eavesdroppers, the wireless channel condition, and the eavesdropper’s operating mode as input data. The second one provides the hop count distribution and the connection probability of the obtained multi-hop path of the first algorithm by averaging a huge number of network topology trials. So far, this paper is the first work that investigates both connectivity and hop count of security-aware multi-hop AHWNs. Moreover, these characteristics of multi-hop AHWNs with colluding eavesdroppers are compared with those of multi-hop AHWNs with non-colluding eavesdroppers and without eavesdroppers. Simulation results show that putting more legitimate users does not greatly improve the quality of the multi-hop path in the non-colluding case compared with that in colluding case. Furthermore, the shape parameter of Nakagami fading has a more substantial effect on the connectivity and hop count than the spread parameter. The results in this paper provide valuable insights in designing and evaluating security-aware multi-hop AHWNs.

连接性和跳数是动态无线网络（例如自组织无线网络 (AHWN)）的两个关键属性。当考虑安全问题时，在 AHWN 中建立安全的多跳路径具有挑战性，因为与先前节点具有无线链路的中间节点可能无法安全地从这些节点接收数据，反之亦然。在本文中，随机几何图形被用来模拟窃听者存在的AHWNs，然后提出一种基于仿真的分析方法来研究连接性、跳数分布、平均跳数的特征以及它们在各种场景下的关系。所提出的基于仿真的分析方法由两种算法组成。第一个找到被选为源和目的地的任意两个合法用户之间所有可能的安全通信路径，并返回最短路径的跳数。该算法利用合法用户和窃听者的随机位置、无线信道条件和窃听者的操作模式作为输入数据。第二个通过对大量网络拓扑试验进行平均，提供第一个算法获得的多跳路径的跳数分布和连接概率。到目前为止，本文是第一项研究安全感知多跳 AHWN 的连接性和跳数的工作。此外，将具有共谋窃听者的多跳 AHWN 的这些特征与具有非共谋窃听者和没有窃听者的多跳 AHWN 的特征进行了比较。仿真结果表明，与共谋情况相比，在非共谋情况下放置更多合法用户并没有大大提高多跳路径的质量。此外，与扩展参数相比，Nakagami 衰落的形状参数对连通性和跳数的影响更大。本文的结果为设计和评估安全感知多跳 AHWN 提供了宝贵的见解。