Mapping directed networks
Mapping directed networks
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映射有向网络
DOI：
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发表时间：
2010
期刊：
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通讯作者：
Alan Taylor
中科院分区：
文献类型：
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作者：
J. J. Crofts;Ernesto Estrada;D. Higham;Alan Taylor
我们开发并测试了一种新的映射，可以应用于有向无加权网络。虽然不是经典矩阵理论意义上的“矩阵函数”，但这种映射将具有零或一项的非对称矩阵转换为具有相同维数的对称实值矩阵，通常具有正负项。该映射旨在揭示复杂有向网络内的近似有向二部群落；每个这样的社区由两组节点S1和S2组成，涉及这些节点的连接主要是从S1中的一个节点到S2中的一个节点。新的映射是通过交替行走的概念来激发的，交替行走依次尊重连接的方向，然后违反连接的方向。考虑到这些行走的组合，我们得到一个矩阵，可以通过原始邻接矩阵和双曲函数的奇异值分解来整齐地表示。我们认为这种新的矩阵映射比其他基于指数的度量有优势。在合成数据上说明了它的性能，然后我们表明它能够揭示神经科学网络中有意义的有向二部子结构。
We develop and test a new mapping that can be applied to directed unweighted networks. Although not a “matrix function” in the classical matrix theory sense, this mapping converts an unsymmetric matrix with entries of zero or one into a symmetric real-valued matrix of the same dimension that generally has both positive and negative entries. The mapping is designed to reveal approximate directed bipartite communities within a complex directed network; each such community is formed by two set of nodes S1 and S2 such that the connections involving these nodes are predominantly from a node in S1 and to a node in S2. The new mapping is motivated via the concept of alternating walks that successively respect and then violate the orientations of the links. Considering the combinatorics of these walks leads us to a matrix that can be neatly expressed via the singular value decomposition of the original adjacency matrix and hyperbolic functions. We argue that this new matrix mapping has advantages over other, exponential-based measures. Its performance is illustrated on synthetic data, and we then show that it is able to reveal meaningful directed bipartite substructure in a network from neuroscience.