The operability of a network concerns its ability to remain operational, despite possible failures in its links or equipment. One may model the network through a graph to evaluate and increase this operability. Its vertices and edges correspond to the users equipment and their connections, respectively. In this article, the problem addressed is identifying the topological change in the graph that leads to a greater increase in the operability of the associated network, considering the case in which failure occurs in the network equipment only. More specifically, we propose two spectral heuristics to improve the vertex reliability in graphs through a single edge insertion. The performance these heuristics and others that are usually found in the literature are evaluated by computational experiments with 22000 graphs of orders 10 up to 20, generated using the Models Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz. From the experiments, it can be observed through analysis and application of statistical test, that one of the spectral heuristics presented a superior performance in relation to the others.

翻译：网络的可操作性在于它是否有能力继续运行,尽管其链接或设备可能存在故障。我们可以通过一个图表来模拟网络,以评估和增加这种可操作性。它的脊椎和边缘分别与用户设备及其连接相对应。在本条中,所处理的问题是确定图中的地形变化导致相关网络的可操作性增加,同时考虑到仅网络设备中发生故障的情况。更具体地说,我们建议用两个光谱超常性能来通过单一边缘插入提高图中脊椎的可靠性。通常在文献中发现的这些超常性能和其他特征的性能,通过22000年的指令10至20图的计算实验进行评估,这些图是使用模型Erdos-Renyi、Barabasi-Albert和Watts-Strogatz生成的。从实验中可以看出,通过分析和应用统计测试,一个光谱超常显示与其他特征相比,光谱性能优异。