McDonnell Mark D, Yaveroğlu Ömer Nebil, Schmerl Brett A, Iannella Nicolangelo, Ward Lawrence M
Computational and Theoretical Neuroscience Laboratory, Institute for Telecommunications Research, University of South Australia, Mawson Lakes, South Australia, Australia; Department of Psychology and Brain Research Centre, University of British Columbia, Vancouver, British Columbia, Canada.
California Institute of Telecommunications and Information Technology (Calit2), University of California Irvine, Irvine, California, United States of America.
PLoS One. 2014 Dec 8;9(12):e114503. doi: 10.1371/journal.pone.0114503. eCollection 2014.
Complex networks are frequently characterized by metrics for which particular subgraphs are counted. One statistic from this category, which we refer to as motif-role fingerprints, differs from global subgraph counts in that the number of subgraphs in which each node participates is counted. As with global subgraph counts, it can be important to distinguish between motif-role fingerprints that are 'structural' (induced subgraphs) and 'functional' (partial subgraphs). Here we show mathematically that a vector of all functional motif-role fingerprints can readily be obtained from an arbitrary directed adjacency matrix, and then converted to structural motif-role fingerprints by multiplying that vector by a specific invertible conversion matrix. This result demonstrates that a unique structural motif-role fingerprint exists for any given functional motif-role fingerprint. We demonstrate a similar result for the cases of functional and structural motif-fingerprints without node roles, and global subgraph counts that form the basis of standard motif analysis. We also explicitly highlight that motif-role fingerprints are elemental to several popular metrics for quantifying the subgraph structure of directed complex networks, including motif distributions, directed clustering coefficient, and transitivity. The relationships between each of these metrics and motif-role fingerprints also suggest new subtypes of directed clustering coefficients and transitivities. Our results have potential utility in analyzing directed synaptic networks constructed from neuronal connectome data, such as in terms of centrality. Other potential applications include anomaly detection in networks, identification of similar networks and identification of similar nodes within networks. Matlab code for calculating all stated metrics following calculation of functional motif-role fingerprints is provided as S1 Matlab File.
复杂网络通常由用于计算特定子图数量的指标来表征。我们将这一类别的一个统计量称为“基序-角色指纹”，它与全局子图计数的不同之处在于，它计算的是每个节点参与的子图数量。与全局子图计数一样，区分“结构型”（诱导子图）和“功能型”（部分子图）的基序-角色指纹可能很重要。在这里，我们通过数学证明，所有功能型基序-角色指纹的向量可以很容易地从任意有向邻接矩阵中获得，然后通过将该向量乘以一个特定的可逆转换矩阵，将其转换为结构型基序-角色指纹。这一结果表明，对于任何给定的功能型基序-角色指纹，都存在唯一的结构型基序-角色指纹。对于没有节点角色的功能型和结构型基序指纹以及构成标准基序分析基础的全局子图计数的情况，我们也证明了类似的结果。我们还明确强调，基序-角色指纹是量化有向复杂网络子图结构的几个流行指标的基础，包括基序分布、有向聚类系数和传递性。这些指标与基序-角色指纹之间的关系还暗示了有向聚类系数和传递性的新亚型。我们的结果在分析由神经元连接组数据构建的有向突触网络方面具有潜在的实用价值，例如在中心性方面。其他潜在应用包括网络中的异常检测、相似网络的识别以及网络中相似节点的识别。作为S1 Matlab文件提供了在计算功能型基序-角色指纹之后计算所有所述指标的Matlab代码。
