Spectral analysis and neural field theory are used to investigate the role of local connections in brain connectivity matrices (CMs) that quantify connectivity between pairs of discretized brain regions. This work investigates how the common procedure of omitting such self-connections (i.e., the diagonal elements of CMs) in published studies of brain connectivity affects the properties of functional CMs (fCMs) and the mutually consistent effective CMs (eCMs) that correspond to them. It is shown that retention of self-connections in the fCM calculated from two-point activity covariances is essential for the fCM to be a true covariance matrix, to enable correct inference of the direct total eCMs from the fCM, and to ensure their compatibility with it; the deCM and teCM represent the strengths of direct connections and all connections between points, respectively. When self-connections are retained, inferred eCMs are found to have net inhibitory self-connections that represent the local inhibition needed to balance excitation via white matter fibers at longer ranges. This inference of spatially unresolved connectivity exemplifies the power of spectral connectivity methods, which also enable transformation of CMs to compact diagonal forms that allow accurate approximation of the fCM and total eCM in terms of just a few modes, rather than the full \(N^2\) CM entries for connections between N brain regions. It is found that omission of fCM self-connections affects both local and long-range connections in eCMs, so they cannot be omitted even when studying the large-scale. Moreover, retention of local connections enables inference of subgrid short-range inhibitory connectivity. The results are verified and illustrated using the NKI-Rockland dataset from the University of Southern California Multimodal Connectivity Database. Deletion of self-connections is common in the field; this does not affect case-control studies but the present results imply that such fCMs must have self-connections restored before eCMs can be inferred from them.

光谱分析和神经场理论用于研究局部连接在大脑连接矩阵 (CM) 中的作用，该矩阵量化离散化大脑区域对之间的连接。这项工作调查了在已发表的大脑连接研究中省略这种自连接（即 CM 的对角线元素）的常见程序如何影响功能 CM (fCM) 和与其对应的相互一致的有效 CM (eCM) 的特性. 结果表明，在根据两点活动协方差计算的 fCM 中保留自连接对于 fCM 成为真正的协方差矩阵至关重要，以便能够从 fCM 正确推断直接总 eCM，并确保它们与它; deCM 和 teCM 代表直接连接和点之间所有连接的强度，分别。当保留自连接时，发现推断的 eCM 具有净抑制性自连接，代表了在更长的范围内通过白质纤维平衡激发所需的局部抑制。这种空间未解析连通性的推断体现了光谱连通性方法的强大功能，这也使 CM 能够转换为紧凑的对角线形式，从而仅根据几种模式而不是完整的模式来精确逼近 fCM 和总 eCM\(N^2\)用于N 个大脑区域之间连接的 CM 条目。发现fCM自连接的省略会影响eCM中的局部和远程连接，因此即使在研究大规模时也不能省略它们。此外，保留本地连接可以推断子网格短程抑制连接。使用来自南加州大学多模式连接数据库的 NKI-Rockland 数据集验证和说明了结果。自连接的删除在该领域很常见；这不会影响病例对照研究，但目前的结果表明，此类 fCM 必须先恢复自连接，然后才能从中推断出 eCM。