论文标题
在复杂网络上的离散时间量子步行以供社区检测
Discrete-time quantum walk on complex networks for community detection
论文作者
论文摘要
我们在复杂网络上定义了离散的量子步行，并将其用于社区检测。我们从数字上表明，与傅立叶硬币的量子步行位于初始节点所属的社区中。同时，与Grover硬币一起使用的量子步行往往是在最初的节点周围定位的，而不是在社区上。在同一网络上，经典随机行走的可能性通常会在休闲时间收敛到均匀分布。因此，我们声称，复杂网络上傅立叶量量子步行的概率的时间平均值比Grover-Coin量子步行和经典随机步行的快照更明确地揭示了社区结构。我们首先展示了针对典型的三社区网络的社区检测方法，从而产生了正确的分组。然后，我们将方法应用于两个现实世界网络，即Zachary的空手道俱乐部和美国机场网络。我们成功地揭示了社区结构，教练的两个社区和后者的主要航空公司的管理员。
We define the discrete-time quantum walk on complex networks and utilize it for community detection. We numerically show that the quantum walk with the Fourier coin is localized in a community to which the initial node belongs. Meanwhile, the quantum walk with the Grover coin tends to be localized around the initial node, not over a community. The probability of the classical random walk on the same network converges to the uniform distribution with a relaxation time generally a priori. We thus claim that the time average of the probability of the Fourier-coin quantum walk on complex networks reveals the community structure more explicitly than that of the Grover-coin quantum walk and a snapshot of the classical random walk. We first demonstrate our method of community detection for a prototypical three-community network, producing the correct grouping. We then apply our method to two real-world networks, namely Zachary's karate club and the US Airport network. We successfully reveals the community structure, the two communities of the instructor and the administrator in the former and major airline companies in the latter.
