Graphs are a powerful mathematical model, and they are used to represent real-world structures in various fields. In many applications, real-world structures with high connectivity and robustness are preferable. For enhancing the connectivity and robustness of graphs, two operations, adding edges and anchoring nodes, have been extensively studied. However, merging nodes, which is a realistic operation in many scenarios (e.g., bus station reorganization, multiple team formation), has been overlooked. In this work, we study the problem of improving graph cohesiveness by merging nodes. First, we formulate the problem mathematically using the size of the $k$-truss, for a given $k$, as the objective. Then, we prove the NP-hardness and non-modularity of the problem. After that, we develop BATMAN, a fast and effective algorithm for choosing sets of nodes to be merged, based on our theoretical findings and empirical observations. Lastly, we demonstrate the superiority of BATMAN over several baselines, in terms of speed and effectiveness, through extensive experiments on fourteen real-world graphs.

翻译：图是一种强大的数学模型，用于表示不同领域的现实世界结构。在许多应用中，具有高连通性和鲁棒性的现实世界结构更受青睐。为增强图的连通性和鲁棒性，添加边和锚定节点这两种操作已被广泛研究。然而，合并节点——在许多场景（如公交站重组、多团队组建）中是一种现实操作——却被忽视了。本文研究通过合并节点改善图凝聚性的问题。首先，我们以给定$k$值下的$k$-桁架规模为目标，对问题进行数学形式化。接着，我们证明该问题的NP难度和非模性。然后，基于理论发现和实证观察，我们提出BATMAN——一种快速有效的算法，用于选择待合并的节点集合。最后，通过在十四个真实世界图上的大量实验，我们展示了BATMAN在速度和有效性方面相较于多个基线的优越性。