Understanding Multiplication of a Matrix with 1 (indicator function?)

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I am reviewing a few machine learning papers that involve graphs. I am having a difficult time understanding what these papers mean by multiplying a matrix (C in the examples shown) by "1" (which I assume is the indicator function).

Is this "1" actually the indicator function or something else I'm completely unaware of? What do these statements mean (matrix multiplied by 1 equating 1).

Thanks in advance :)