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Abstract:
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The concept of sparsity has received much attention in the study of networks. While various formulations of sparsity can be found in the literature, all involve the relative cardinalities of the vertex set and the edge set. The semantics of the word "sparse" -- the property of being widely scattered or thinly distributed -- has motivated a corresponding, informal notion for networks; namely, a description of those networks which exhibit "not too many" edges. As such, the concept of sparsity has gained popularity due in part to widespread anecdotal observation that in many real-world networks, vertices tend to exhibit low degree relative to the cardinality of the underlying vertex set. We investigate the connection between established notions of sparsity and large sample approximation for networks; in particular, we address the extent to which sparsity impacts subsequent inference.
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