Detection of core-periphery structure in networks using spectral methods and geodesic paths
Detection of core-periphery structure in networks using spectral methods and geodesic paths
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DOI：
10.1017/s095679251600022x
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发表时间：
2016-12-01
影响因子：
1.9
通讯作者：
Porter, Mason A.
中科院分区：
文献类型：
--
作者：
Cucuringu, Mihai;Rombach, Puck;Porter, Mason A.
我们引入了几种新颖和计算有效的方法，用于检测网络中的“核心 - 外围结构”。核心外围结构是一种中尺度结构，由密集连接的核心顶点和稀疏连接的外围顶点组成。核心顶点往往彼此之间和外围顶点均息息相关，这些顶点往往与其他顶点没有很好的联系。我们的第一种方法基于网络中的运输，从网络中的许多测量路径汇总信息，并为每个顶点产生一个分数，以反映该顶点是核心顶点的可能性。我们的第二种方法是基于网络邻接矩阵的低级别近似值，我们表达为张量生产矩阵的扰动。我们的第三种方法使用随机步行拉普拉斯式的底部特征向量来推断出核心评分，并将分类为核心和外围顶点。我们还将目标函数设计为（1）帮助将顶点分类为核心或外围顶点，（2）为分类为核心与外围顶点提供了拟合优度标准。为了检查我们的方法的性能，我们将算法应用于合成生成的网络和由现实世界数据集构建的各种网络。
We introduce several novel and computationally efficient methods for detecting "core-periphery structure" in networks. Core-periphery structure is a type of mesoscale structure that consists of densely connected core vertices and sparsely connected peripheral vertices. Core vertices tend to be well-connected both among themselves and to peripheral vertices, which tend not to be well-connected to other vertices. Our first method, which is based on transportation in networks, aggregates information from many geodesic paths in a network and yields a score for each vertex that reflects the likelihood that that vertex is a core vertex. Our second method is based on a low-rank approximation of a network's adjacency matrix, which we express as a perturbation of a tensor-product matrix. Our third approach uses the bottom eigenvector of the random-walk Laplacian to infer a coreness score and a classification into core and peripheral vertices. We also design an objective function to (1) help classify vertices into core or peripheral vertices and (2) provide a goodness-of-fit criterion for classifications into core versus peripheral vertices. To examine the performance of our methods, we apply our algorithms to both synthetically generated networks and a variety of networks constructed from real-world data sets.