The rapid spread of learning networks based on asynchronous written communication--Asynchronous Learning Networks (ALNs)--makes it crucial to assess the possibilities offered by these new environments to facilitate and promote learning processes and learning outcomes. Our interest in this area is specifically directed towards the study of distributed teaching presence understood as the exercise of educational influence, i.e. as the help provided to each other participant in an ALN to promote individual and collective learning. We adopt a multi-method approach that integrates the structural analysis of presence (access and participation) and connectivity (reciprocity and responsiveness) with the content analysis of the participants' contributions. This article focuses on structural analysis as a relevant and powerful tool for the study of collaborative learning in networking and asynchronous contexts. Its main objective is to show how a relevant and useful system of indicators and profiles, which identify and examine the distribution of educational influence in ALNs, can be constructed. We present the theoretical assumptions surrounding the concept of distributed teaching presence and illustrate the analysis with data from two didactic sequences in higher education. The results show that the structural analysis, when theoretically grounded and oriented, is a powerful tool for identifying different activity profiles related to different levels and modalities of the exercise of educational influence and for assessing the distributed teaching presence in learning networks. Finally, we discuss the benefits and constraints of this kind of analysis.