Triangle counting in a graph is a fundamental problem and has a wide range of applications in various domains. It is crucial in understanding the structural properties of a graph and is often used as a building block for more complex graph analytics. In this paper, we solve the triangle counting problem in an anonymous graph in a distributed setting using mobile agents and subsequently use this as a subroutine to tackle the truss decomposition and triangle centrality problem. The paper employs mobile agents, placed on the nodes of the graph to coordinate among themselves to solve the triangle enumeration problem for the graph. Following the literature, we consider the synchronous systems where each robot executes its tasks concurrently with all others and hence time complexity can be measured as the number of rounds needed to complete the task. The graph is anonymous, i.e., without any node labels or IDs, but the agents are autonomous with distinct IDs and have limited memory. Agents can only communicate with other agents locally i.e., if and only if they are at the same node. The goal is to devise algorithms that minimise both the time required for triangle counting and the memory usage at each agent. We further demonstrate how the triangle count obtained through the mobile agent approach can be leveraged to address the truss decomposition, triangle centrality and local clustering coefficient problems, which involves finding maximal sub-graphs with strong interconnections. Truss decomposition helps in identifying maximal, highly interconnected sub-graphs, or trusses, within a network, thus, revealing the structural cohesion and tight-knit communities in complex graphs, facilitating the analysis of relationships and information flow in various fields, such as social networks, biology, and recommendation systems.

翻译：图的三角形计数是一个基础性问题，在多个领域具有广泛应用。它对于理解图的结构特性至关重要，常被用作更复杂图分析的构建模块。本文通过移动智能体在分布式环境下解决匿名图中的三角形计数问题，并以此作为子程序处理桁架分解与三角形中心性问题。本文采用部署在图节点上的移动智能体相互协调，解决图的三角形枚举问题。遵循已有文献，我们考虑同步系统，其中每个机器人与其他机器人同时执行任务，因此时间复杂度可通过完成任务所需的轮数来衡量。图是匿名的，即没有节点标签或ID，但智能体是自治的，具有唯一ID和有限内存。智能体仅能局部通信，即只有当它们位于同一节点时才能相互通信。目标是设计算法，最小化三角形计数所需时间及每个智能体的内存使用量。我们进一步展示如何利用通过移动智能体方法获得的三角形计数来解决桁架分解、三角形中心性和局部聚类系数问题，这些问题涉及寻找具有强互连性的最大子图。桁架分解有助于识别网络中最大且高度互连的子图（即桁架），从而揭示复杂图中的结构凝聚性和紧密社区，促进社交网络、生物学和推荐系统等领域中关系与信息流的分析。