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Hello,

I am trying to sort out the implications of sampling from a known set of 
ties in link-tracing designs with an unknown total node-set and would 
appreciate help or related references.

For example, a web-crawler might be designed to sample 10% of the links 
on a given webpage. The seed nodes are known and the nodes that the 
crawler could sample from at each step are known (and if/when those 
nodes also appear in subsequent sampled pages' links), but the total 
population of nodes is not known.

Is it possible to draw legitimate conclusions on network properties from 
such a data set, perhaps by using the sampling probabilities at each 
stage of the design in a weighting system? Or does the nature of the 
non-random selection on the dependent variable preclude such analysis?

Work I have found on link-tracing designs in ERGM (Pattison et al 2012, 
Handcock and Gile 2010, Koskinen et al 2013) assumes that sampling takes 
place on nodes but not ties, e.g. that link-tracing designs exhaustively 
sample the ties from given node-sets. Respondent Driven Sampling uses 
link tracing without the assumption of exhaustive sampling, but with 
non-sampled ties unknown (and other restrictions that limit the ability 
to draw conclusions about the network itself).

The end goals of this question are twofold:
(1) To collect multi-wave online link-tracing data for network analysis 
with less strain on (the collector's) computer resources and (the pages 
of interest's) server resources
(2) I'm also hoping that if it were simpler to collect valid network 
data with greater depth (number of waves) without producing as 
intimidatingly large data sets, it might encourage more social 
scientists without extensive computer science or mathematical 
backgrounds to pursue internet-originated structural data that is 
relevant to their research questions

Thanks for any help you have to offer.

Sincerely,
Nathaniel Porter
Department of Sociology, Penn State University <http://sociology.la.psu.edu>
Research Associate, The Association of Religion Data Archives 
<http://thearda.com>

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