Social semiotic discussion about the role played by representations in effective teaching and learning in areas such as physics have led to theoretical proposals that have a strong common thread: in order to acquire an appropriate understanding of a particular object of learning, access to the disciplinary relevance aspects in the representations used calls for the attainment of representational competence across a particular critical {constellation of systematically used semiotic resources (which are referred to as }modes{, see more on this later)}. However, an affirming empirical investigation into the relationship between a particular object of learning and different representational formulations, particularly with large numbers of students, is missing in the literature, especially in the context of university-level physics education. To start to address this research shortfall the positioning for this article is that such studies need to embrace the complexities of student thinking and application of knowledge. To achieve this, both factor and network analyses were used. Even though both approaches are grounded in different frameworks, for the task at hand, both approaches are useful for analyzing clustering dynamics within the responses of a large number of participants. Both also facilitate an exploration of how such clusters may relate to the semiotic resource formulation of a representation. The data was obtained from a questionnaire given to 1368 students drawn from 12 universities across seven countries. The questionnaire deals with the refraction of light in introductory-level physics and involves asking students to give their best prediction of the relative visual positioning of images and objects in different semiotically constituted situations. The results of both approaches revealed no one-to-one relationship between a particular representational formulation and a particular cluster of student responses. The factor analysis used correct answer responses to reveal clusters that brought to the fore three different complexity levels in relation to representation formulation. The network analysis used all responses (correct and incorrect) to reveal three structural patterns. What is evident from the results of both analyses is that they confirm two broad conclusions that have emerged from social semiotic explorations dealing with representations in relation to attempting to optimize teaching and learning. The first, which is linked to a facilitating-awareness perspective, is that any given disciplinary visual representation can be expected to evoke a dispersed set of knowledge structures, which is referred to as their relevance structure. Thus, the network analysis results can be seen as presenting a unique starting point for studies aiming to identify such relevance structure. The second broad conclusion is that disciplinary visual representation can and often do, contain more disciplinary-relevant aspects than what may be directly visible in a given representation. These are referred to as the appresent aspects that need to become part of the total awareness needed by someone to constitute an intended meaning. The results of the factor analysis can then also be seen to be a way of capturing all the disciplinary-relevant aspects (both present and appresent). Educational implications are discussed.