Generalized blockmodeling of valued networks

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Generalized blockmodeling of valued networks extends blockmodeling to networks with weighted ties (not just 0/1). Traditional ideal blocks are binary, so comparing a valued network directly to binary patterns is not straightforward. To handle this, a non-parametric approach uses an optional parameter that sets how prominent a valued tie must be, based on the percentile deviation between observed and expected flows. This two‑sided setup can produce ties that are neither clearly present nor absent, which changes how we measure differences between the empirical blocks and their ideal forms.

To keep the interpretation clear, the approach proposes a maximum two‑sided deviation threshold that keeps overall interpretational uncertainty near zero. In effect, the optional parameter can act like a state indicating whether a block is interpretable or not.

Because standard ideal blocks are binary, matching them to valued data is difficult. One simple workaround is to dichotomize the network. However, starting in 2007 Aleš Žiberna introduced valued (generalized) blockmodeling and a related homogeneity blockmodeling. The key idea is that a block’s inconsistency can be measured by the within‑block variability of the values.

Two more approaches were proposed by Carl Nordlund in 2019: the deviational approach and the correlation‑based generalized approach. Both compare valued networks with the ideal block while ignoring the actual values, which preserves more information and leads to fewer partitions with identical criterion values. As a result, generalized blockmodeling of valued networks can measure inconsistencies more precisely, often yielding a single optimal partition—especially with homogeneity blockmodeling—whereas binary blockmodeling on the same data often produces multiple optimal partitions.