Background: Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks  related to their biological functions. However, there is disagreement on the statistical significance of these motifs and the methods used to determine it . Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over ten years ago but have had limited application  , possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. Results: We illustrate the application of these methods to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks. We confirm the over-representation of triangles in the PPI network and transitive triangles (feed-forward loop) in an E. coli regulatory network, but not in a yeast regulatory network. We also confirm using this method previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features . Conclusion: ERGMs allow the over- or under-representation of multiple non-independent structural configurations to be tested simultaneously in a single model. This can overcome some of the problems recently identified in mainstream methods for motif identification, specifically assumptions of normally distributed motif frequencies and independence of motifs .
 Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks , related to their biological functions. However, there is disagreement as to the statistical significance of these motifs , and there are potential problems with standard methods for estimating this significance . Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over ten years ago but have had limited application to biological networks , possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network , and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm , using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features .
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Background:
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to biological networks
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. Conclusion: ERGMs allow the over- or under-representation of multiple non-independent structural configurations to be tested simultaneously in a single model. This can overcome some of the problems recently identified in mainstream methods for motif identification, specifically assumptions of normally distributed motif frequencies and independence of motifs