Modern data analytics applications on graphs often operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the problem solution. Part III of this monograph starts by a comprehensive account of ways to learn the pertinent graph topology, ranging from the simplest case where the physics of the problem already suggest a possible graph structure, through to general cases where the graph structure is to be learned from the data observed on a graph. A particular emphasis is placed on the use of standard “relationship measures” in this context, including the correlation and precision matrices, together with the ways to combine these with the available prior knowledge and structural conditions, such as the smoothness of the graph signals or sparsity of graph connections. Next, for learning sparse graphs (that is, graphs with a small number of edges), the utility of the least absolute shrinkage and selection operator, known as (LASSO) is addressed, along with its graph specific variant, the graphical LASSO. For completeness, both variants of LASSO are derived in an in
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