A key concern in both neuroscience and machine learning is how the connectivity features of networks drive dynamics and computation in biological and artificial neural networks. Previous research has followed two complementary approaches to quantify the structure in connectivity: either from the perspective of biological experiments by characterizing the local statistics of connectivity motifs between small groups of neurons; or from the perspective of artificial neural networks by leveraging the network-wide low-rank patterns of connectivity that influence the resulting low-dimensional dynamics. Both approaches point to mechanisms by means of which the network connectivity offers a degree of control over the space of activity patterns and the network dynamics. However, there has not been much exploration done on the direct relationships between these two, thus it is still not apparent how local connectivity statistics relate to the global connectivity structure and affect the network dynamics. To bridge this gap, here we develop an analytical method for mapping locally-defined biological connectivity statistics onto an approximate global low-rank structure. Our approach allows us to disentangle the effects of mean connectivity and multiple types of second-order motifs on global recurrent feedback and feedforward propagation, providing an intuitive picture of how local connectivity shapes global network dynamics.