We develop unbiased strategies to probabilistic T-wave snowball sampling from graphs, where the interest of estimation may concern finite-order subgraphs such as triangles, cycles or stars. Our approaches encompass also the finite-population sampling strategies to multiplicity sampling and adaptive cluster sampling, both of which can be recast as snowball sampling aimed at graph node totals. A general snowball sampling theory offers greater flexibility in terms of scope and efficiency of graph sampling, in addition to the existing random node or edge sampling methods.

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