This study defines and detects competitive and complementary links in a complex network and constructs theories illustrating how the variation of traffic flow is interconnected with network structure. To test the hypotheses, we extract a grid-like sub-network containing 140 traffic links from the Minneapolis - St. Paul highway system. We reveal a real-world traffic network comprises both competitive and complementary links, and there is a negative network dependency between a competitive link pair and a positive network dependency between a complementary link pair. We validate a robust linear relationship between standard deviation of flow in a link and its number of competitive links, its link correlation with competitive links, and its network dependency with both competitive and complementary links. The results indicate the number of competitive links in a traffic network is negatively correlated with the variation of traffic flow in congested regimes as drivers are able to take alternative paths. The results also signify that the more the traffic flow of a link is correlated to the traffic flow of its competitive links, the more the flow variation is in the link. Considering the network dependency, however, it is corroborated that the more the network dependency between a link and its competitive links, the more the flow variation in the link. This is also true for complementary links.