及物性的拆除与社交网络的崩溃
Transitivity Demolition and the Falls of Social Networks
摘要：
在本文中，我们研究了一个复杂网络的关键要素，即它的节点和连接，在保持网络的结构和功能下，节点和边缘的意外结构扰动的关键作用删除。具体来说，我们要确定关键节点和边，它们的故障（随机或故意的）将破坏网络中最多的连接三元组（或三角形）。这个问题非常重要，因为连通三元组构成了许多现实世界系统中强连接的基础，例如社交网络中的相互关系，通信网络中的可靠数据传输以及移动网络中的稳定路由策略。断开的三元组，类似于断开的相互连接，可以极大地影响网络的结构并破坏其正常功能，这可能进一步导致整个系统的损坏。对这些关键因素的分析将揭示许多复杂系统在实践中的复原力和稳健性背后的关键因素。我们制定了多个优化问题下的分析，并显示其棘手性。接下来，我们提出了有效的近似算法，即DAK-n和DAK-e，保证了$(1-1/e)$近似比（与整体最优解相比），同时具有与幂律网络上的最佳三角形计数和列表算法相同的时间复杂度。这一优势使得我们的算法即使在非常大的网络中也能很好地扩展。从应用的角度来看，我们对具有数百万个节点和数十亿条边的真实社交痕迹进行了全面的实验。这些实证实验表明，我们的方法实现了更好的结果，同时比当前最先进的方法快100倍。
英文摘要：
In this paper, we study crucial elements of a complex network, namely its nodes and connections, which play a key role in maintaining the network's structure and function under unexpected structural perturbations of nodes and edges removal. Specifically, we want to identify vital nodes and edges whose failure (either random or intentional) will break the most number of connected triples (or triangles) in the network. This problem is extremely important because connected triples form the foundation of strong connections in many real-world systems, such as mutual relationships in social networks, reliable data transmission in communication networks, and stable routing strategies in mobile networks. Disconnected triples, analog to broken mutual connections, can greatly affect the network's structure and disrupt its normal function, which can further lead to the corruption of the entire system. The analysis of such crucial elements will shed light on key factors behind the resilience and robustness of many complex systems in practice. We formulate the analysis under multiple optimization problems and show their intractability. We next propose efficient approximation algorithms, namely DAK-n and DAK-e, which guarantee an $(1-1/e)$-approximate ratio (compared to the overall optimal solutions) while having the same time complexity as the best triangle counting and listing algorithm on power-law networks. This advantage makes our algorithms scale extremely well even for very large networks. In an application perspective, we perform comprehensive experiments on real social traces with millions of nodes and billions of edges. These empirical experiments indicate that our approaches achieve comparably better results while are up to 100x faster than current state-of-the-art methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
