In the paper I am reading, the author has not provided a "methodology" for visualising what a $p$-chain looks like; a google search has not yield anything to assist me in this either. Persistent Homology: An Introduction and a New Text Representation for Natural Language Processing
To get started, the definition for a $p$-chain is as follows:
Definition: A $p$-chain is a subset of $p$-simplicies in a simplicial complex K
But how does this subset looks like? The author provided a couple of images
with the left image being a 2 - chain and the right being a 1 - chain? How do I convince myself of this?