Previous research on simulated ecological networks has often focused on issues such as the distribution of the number of links between species, without generally categorizing the types of inter-species relationships that develop, unless those relationships are of some predesigned form (e.g., food webs). In this work we use a model system to examine general, dynamically-evolved ecological networks that are subject to occasional invasion by novel species. Keeping track of the specific types and numbers of interactions between species over time leads to insight on how these affect network stability, fragility and evolution. We discuss the role that assembly rules play on the evolutionary trajectories of randomly initialized communities. We also investigate the occurrence of certain types of interactions (e.g., cyclic) and quantify their destabilizing effect on the network. In particular, extinctions and secondary extinctions (``avalanches'') are related to these issues.