A major task for postgenomic systems biology researchers is to systematically catalogue molecules and their interactions within living cells. Advancements in complex-network theory are being made toward uncovering organizing principles that govern cell formation and evolution, but we lack understanding of how molecules and their interactions determine how complex systems function. Molecular bridge motifs include isolated motifs that neither interact nor overlap with others, whereas brick motifs act as network foundations that play a central role in defining global topological organization. To emphasize their structural organizing and evolutionary characteristics, we define bridge motifs as consisting of weak links only and brick motifs as consisting of strong links only, then propose a method for performing two tasks simultaneously, which are as follows: 1) detecting global statistical features and local connection structures in biological networks and 2) locating functionally and statistically significant network motifs. To further understand the role of biological networks in system contexts, we examine functional and topological differences between bridge and brick motifs for predicting biological network behaviors and functions. After observing brick motif similarities between E. coli and S. cerevisiae, we note that bridge motifs differentiate C. elegans from Drosophila and sea urchin in three types of networks. Similarities (differences) in bridge and brick motifs imply similar (different) key circuit elements in the three organisms. We suggest that motif-content analyses can provide researchers with global and local data for real biological networks and assist in the search for either isolated or functionally and topologically overlapping motifs when investigating and comparing biological system functions and behaviors.