基于信息副本相关的多分辨率巨型网络社团检测
Multiresolution community detection for megascale networks by information-based replica correlations
摘要：
我们使用一个波茨模型社区检测算法，以准确和定量地评估一个图的层次或多分辨率结构。我们的多分辨率算法计算多个副本之间的相关性（“副本”）的同一个图在一系列的决议。重要的多分辨率结构，确定强相关的副本。平均归一化互信息、信息的变化和其他测量原则上给出“最佳”分辨率的定量估计，并指示图中结构的相对强度。由于该方法基于信息比较，因此原则上可以与可以检查多个分辨率的任何社区检测模型一起使用。我们的方法可以扩展到其他优化问题。作为一种局部度量，我们的Potts模型避免了影响其他流行模型的“分辨率限制”。有了这个模型，我们的社区检测算法的准确性是目前最好的方法之一。使用它，我们可以检查超过4000万个节点和超过10亿条边的图。我们进一步报告说，我们的算法的多分辨率变体可以解决系统的至少20万个节点和10万个边缘在一个处理器上具有非常高的精度。对于典型的情况下，我们发现一个超线性缩放，O（L^{1.3}）社区检测和O（L^{1.3} log N）的多分辨率算法，其中L是边缘的数量和N是系统中的节点数。
英文摘要：
We use a Potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph. Our multiresolution algorithm calculates correlations among multiple copies ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by strongly correlated replicas. The average normalized mutual information, the variation of information, and other measures in principle give a quantitative estimate of the "best" resolutions and indicate the relative strength of the structures in the graph. Because the method is based on information comparisons, it can in principle be used with any community detection model that can examine multiple resolutions. Our approach may be extended to other optimization problems. As a local measure, our Potts model avoids the "resolution limit" that affects other popular models. With this model, our community detection algorithm has an accuracy that ranks among the best of currently available methods. Using it, we can examine graphs over 40 million nodes and more than one billion edges. We further report that the multiresolution variant of our algorithm can solve systems of at least 200000 nodes and 10 million edges on a single processor with exceptionally high accuracy. For typical cases, we find a super-linear scaling, O(L^{1.3}) for community detection and O(L^{1.3} log N) for the multiresolution algorithm where L is the number of edges and N is the number of nodes in the system.
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