Learning a new topic also entails learning its terminology. As a newbie to the subject, I'm amused by chapter headings like "Abstract Simplicial Complex" that seem like an oxymoron :-)
I’m not convinced “abstract” is a good word here, but what they mean is that it doesn’t have any metrical/geometric relationships beyond the graph structure.
FYI the word 'complex' in mathematics is often used similar to it's usage as an English noun - "a whole made up of interrelated parts", e.g. a building complex, apartment complex, military-industrial complex. A 'simplicial complex' is then, informally, "a whole made up of interrelated simplexes".
