Since the spdep package was created, spatial weights objects have been constructed as lists with three components and a few attributes, in old-style class listw objects. The first component of a listw object is an nb object, a list of n integer vectors, with at least a character vector region.id attribute with n unique values (like the row.names of a data.frame object); n is the number of spatial entities. Component i of this list contains the integer identifiers of the neighbours of i as a sorted vector with no duplication and values in 1:n; if i has no neighbours, the component is a vector of length 1 with value 0L. The nb object may contain an attribute indicating whether it is symmetric or not, that is whether i is a neighbour of j implies that j is a neighbour of i. Some neighbour definitions are symmetric by construction, such as contiguities or distance thresholds, others are asymmetric, such as k-nearest neighbours. The nb object redundantly stores both i-j and j-i links.
The second component of a listw object is a list of n numeric vectors, each of the same length as the corresponding non-zero vectors in the nbobject. These give the values of the spatial weights for each i-j neighbour pair. It is often the case that while the neighbours are symmetric by construction, the weights are not, as for example when weights are row-standardised by dividing each row of input weights by the count of neighbours or cardinality of the neighbour set of i. In the nb2listwfunction, it is also possible to pass through general weights, such as inverse distances, shares of boundary lengths and so on.
The third component of a listw object records the style of the weights as a character code, with "B" for binary weights taking values zero or one (only one is recorded), "W" for row-standardised weights, and so on. In order to subset listw objects, knowledge of the style may be necessary
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