Probabilistic models of network growth have been extensively studied as idealized representations of network evolution. Models, such as the Kronecker model, duplication-based models, and preferential attachment models, have been used for tasks such as representing null models, detecting anomalies, algorithm testing, and developing an understanding of various mechanistic growth processes. However, developing a new growth model to fit observed properties of a network is a difficult task, and as new networks are studied, new models must constantly be developed. Here, we present a framework, called GrowCode, for the automatic discovery of novel growth models that match user-specified topological features in undirected graphs. GrowCode introduces a set of basic commands that are general enough to encode several previously developed models. Coupling this formal representation with an optimization approach, we show that GrowCode is able to discover models for protein interaction networks, autonomous systems networks, and scientific collaboration networks that closely match properties such as the degree distribution, the clustering coefficient, and assortativity that are observed in real networks of these classes. Additional tests on simulated networks show that the models learned by GrowCode generate distributions of graphs with similar variance as existing models for these classes.

BACKGROUND: Chromosome conformation capture experiments result in pairwise proximity measurements between chromosome locations in a genome, and they have been used to construct three-dimensional models of genomic regions, chromosomes, and entire genomes. These models can be used to understand long-range gene regulation, chromosome rearrangements, and the relationships between sequence and spatial location. However, it is unclear whether these pairwise distance constraints provide sufficient information to embed chromatin in three dimensions. A priori, it is possible that an infinite number of embeddings are consistent with the measurements due to a lack of constraints between some regions. It is therefore necessary to separate regions of the chromatin structure that are sufficiently constrained from regions with measurements that do not provide enough information to reconstruct the embedding. RESULTS: We present a new method based on graph rigidity to assess the suitability of experiments for constructing plausible three-dimensional models of chromatin structure. Underlying this analysis is a new, efficient, and accurate algorithm for finding sufficiently constrained (rigid) collections of constraints in three dimensions, a problem for which there is no known efficient algorithm. Applying the method to four recent chromosome conformation experiments, we find that, for even stringently filtered constraints, a large rigid component spans most of the measured region. Filtering highlights higher-confidence regions, and we find that the organization of these regions depends crucially on short-range interactions. CONCLUSIONS: Without performing an embedding or creating a frequency-to-distance mapping, our proposed approach establishes which substructures are supported by a sufficient framework of interactions. It also establishes that interactions from recent highly filtered genome-wide chromosome conformation experiments provide an adequate set of constraints for embedding. Pre-processing experimentally observed interactions with this method before relating chromatin structure to biological phenomena will ensure that hypothesized correlations are not driven by the arbitrary choice of a particular unconstrained embedding. The software for identifying rigid components is GPL-Licensed and available for download at http://cbcb.umd.edu/kingsford-group/starfish.