Modern physical networks, for example in communication and transportation, can be interpreted as directed graphs. Network models are used to identify the probability that given nodes are connected, and therefore the effect of a failure at a given link. This is essential for network design, optimization, and reliability. In this study, we investigated three alternative ensembles for estimating network reliability using the Wang–Landau algorithm. The first performed random walks on a structure function having two possible states: connected and disconnected. The second used random walks on a reliability polynomial. The third combined random walks with the average of connecting probabilities. The accuracy and limitations of the three ensembles were compared by estimating the reliability of three network models: a bridge network, a ladder-type network, and a dodecahedron network. The simulation results showed that the use of a random walk on a structure function failed to produce estimates when applied to highly reliable networks in any of the three network types. The other two approaches performed efficiently for bridge or ladder-type networks at any level of network reliability. The random walk on a probability space using the $1∕t$ algorithm was the only ensemble that was able to yield accurate estimates for a dodecahedron network, though even this failed at the highest level of network reliability. The other two methods failed to converge within $10^8$ Monte Carlo trials. The use of the average of connecting probabilities required a shorter computation time when applied to a large network. Methods that can reduce variance for large, highly reliable networks require further investigation.

现代物理网络，例如在通信和运输中，可以解释为有向图。网络模型用于确定给定节点已连接的概率，从而确定给定链路上的故障影响。这对于网络设计，优化和可靠性至关重要。在这项研究中，我们研究了使用Wang-Landau算法估计网络可靠性的三种替代集成。首先在具有两个可能状态的结构函数上执行随机游走：连接和断开。第二个在可靠性多项式上使用随机游动。第三个结合了随机游走与连接概率的平均值。通过估算以下三种网络模型的可靠性，比较了三个合奏的准确性和局限性：网桥网络，梯形网络，和十二面体网络。仿真结果表明，当将随机游走用于结构函数时，当将其应用于三种网络类型中的任何一种时，都无法产生估计值。对于网桥或阶梯型网络，在任何级别的网络可靠性下，其他两种方法都可以有效执行。使用$\mathrm{1个}∕Ť$该算法是唯一能够对十二面体网络进行准确估计的集合，尽管即使这样在网络可靠性的最高级别上也失败了。其他两种方法无法在内部收敛$\mathrm{1个}{0}^8$蒙特卡洛审判。当应用于大型网络时，使用平均连接概率需要较短的计算时间。可以减少大型，高度可靠网络的方差的方法需要进一步研究。