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Consider the network of all secondary structures of a given RNA sequence,where nodes are connected when the corresponding structures have base pairdistance one. The expected degree of the network is the average number ofneighbors, where average may be computed with respect to the either the uniformor Boltzmann probability. Here we describe the first algorithm, RNAexpNumNbors,that can compute the expected number of neighbors, or expected network degree,of an input sequence. For RNA sequences from the Rfam database, the expecteddegree is significantly less than the CMFE structure, defined to have minimumfree energy over all structures consistent with the Rfam consensus structure.The expected degree of structural RNAs, such as purine riboswitches,paradoxically appears to be smaller than that of random RNA, yet the differencebetween the degree of the MFE structure and the expected degree is larger thanthat of random RNA. Expected degree does not seem to correlate with standardstructural diversity measures of RNA, such as positional entropy, ensembledefect, etc. The program {\tt RNAexpNumNbors} is written in C, runs in cubictime and quadratic space, and is publicly available athttp://bioinformatics.bc.edu/clotelab/RNAexpNumNbors.

Expected degree for RNA secondary structure networks