通过随机游动探索复杂网络
Exploring Complex Networks through Random Walks
摘要：
大多数真实的复杂网络--比如蛋白质相互作用、社会联系、互联网--都只是部分地为我们所知和所用。虽然在许多情况下，探索这种网络的过程类似于随机游走，但研究和描述这种网络的节点和边缘如何有效地被不同的策略覆盖成为一个关键问题。与此同时，这是至关重要的，以推断如何以及可以拓扑测量，如平均节点度和平均聚类系数估计在这样的网络探索。本文通过考虑随机和Barabási-Albert（BA）网络模型来解决这些问题，这些模型通过三种类型的随机游走来探索不同的连通性：传统的，优先于未跟踪的边缘，优先于未访问的节点。得到了一系列相关的结果，包括具有相同大小和平均节点度的随机模型和BA模型允许相似的节点和边覆盖效率，确定了覆盖给定百分比的节点/边的随机行走步长与网络大小的线性缩放，以及BA网络上随机游动对平均节点度和聚类系数的估计往往导致严重偏差的结果。许多是这样的结果的理论和实践意义。
英文摘要：
Most real complex networks -- such as protein interactions, social contacts, the internet -- are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key issue to investigate and characterize how effectively the nodes and edges of such networks can be covered by different strategies. At the same time, it is critically important to infer how well can topological measurements such as the average node degree and average clustering coefficient be estimated during such network explorations. The present article addresses these problems by considering random and Barabási-Albert (BA) network models with varying connectivity explored by three types of random walks: traditional, preferential to untracked edges, and preferential to unvisited nodes. A series of relevant results are obtained, including the fact that random and BA models with the same size and average node degree allow similar node and edge coverage efficiency, the identification of linear scaling with the size of the network of the random walk step at which a given percentage of the nodes/edges is covered, and the critical result that the estimation of the averaged node degree and clustering coefficient by random walks on BA networks often leads to heavily biased results. Many are the theoretical and practical implications of such results.
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。
