Sophisticated methods for analysing complex networks promise to be of great benefit to almost all scientific disciplines, yet they elude us. In this work, we make fundamental methodological advances to rectify this. We discover that the interaction between a small number of roles, played by nodes in a network, can characterize a network's structure and also provide a clear real-world interpretation. Given this insight, we develop a framework for analysing and comparing networks, which outperforms all existing ones. We demonstrate its strength by uncovering novel relationships between seemingly unrelated networks, such as Facebook, metabolic, and protein structure networks. We also use it to track the dynamics of the world trade network, showing that a country's role of a broker between non-trading countries indicates economic prosperity, whereas peripheral roles are associated with poverty. This result, though intuitive, has escaped all existing frameworks. Finally, our approach translates network topology into everyday language, bringing network analysis closer to domain scientists.

The Galaxy Zoo 1 catalog displays a bias towards the S-wise winding direction in spiral galaxies which has yet to be explained. The lack of an explanation confounds our attempts to verify the Cosmological Principle, and has spurred some debate as to whether a bias exists in the real universe. The bias manifests not only in the obvious case of trying to decide if the universe as a whole has a winding bias, but also in the more insidious case of selecting which galaxies to include in a winding direction survey. While the former bias has been accounted for in a previous image-mirroring study, the latter has not. Furthermore, the bias has never been corrected in the GZ1 catalog, as only a small sample of the GZ1 catalog was re-examined during the mirror study. We show that the existing bias is a human selection effect rather than a human chirality bias. In effect, the excess S-wise votes are spuriously "stolen" from the elliptical and edge-on-disk categories, not the Z-wise category. Thus, when selecting a set of spiral galaxies by imposing a threshold T so that max(P S , P Z ) > T or P S +P Z > T , we spuriously select more S-wise than Z-wise galaxies. We show that when a provably unbiased machine selects which galaxies are spirals independent of their chirality, the Swise surplus vanishes, even if humans are still used to determine the chirality. Thus, when viewed across the entire GZ1 sample (and by implication, the Sloan catalog), the winding direction of arms in spiral galaxies as viewed from Earth is consistent with the flip of a fair coin.

Given an approximately centered image of a spiral galaxy, we describe an entirely automated method that finds, centers, and sizes the galaxy and then automatically extracts structural information about the spiral arms. For each arm segment found, we list the pixels in that segment and perform a least-squares fit of a logarithmic spiral arc to the pixels in the segment. The algorithm takes about 1 minute per galaxy, and can easily be scaled using parallelism. We have run it on all ∼644,000 Sloan objects classified as "galaxy" and large enough to observe some structure. Our algorithm is stable in the sense that the statistics across a large sample of galaxies vary smoothly based on algorithmic parameters, although results for individual galaxies can sometimes vary in a non-smooth but easily understood manner. We find a very good correlation between our quantitative description of spiral structure and the qualitative description provided by humans via Galaxy Zoo. In addition, we find that pitch angle often varies significantly segment-to-segment in a single spiral galaxy, making it difficult to define "the" pitch angle for a single galaxy. Finally, we point out how complex arm structure (even of long arms) can lead to ambiguity in defining what an "arm" is, leading us to prefer the term "arm segments".

Motivation: Proteins underlay the functioning of a cell and the wiring of proteins in protein–protein interaction network (PIN) relates to their biological functions. Proteins with similar wiring in the PIN (topology around them) have been shown to have similar functions. This property has been successfully exploited for predicting protein functions. Topological similarity is also used to guide network alignment algorithms that find similarly wired proteins between PINs of different species; these similarities are used to transfer annotation across PINs, e.g. from model organisms to human. To refine these functional predictions and annotation transfers, we need to gain insight into the variability of the topology-function relationships. For example, a function may be significantly associated with specific topologies, while another function may be weakly associated with several different topologies. Also, the topology-function relationships may differ between different species.Results: To improve our understanding of topology-function relationships and of their conservation among species, we develop a statistical framework that is built upon canonical correlation analysis. Using the graphlet degrees to represent the wiring around proteins in PINs and gene ontology (GO) annotations to describe their functions, our framework: (i) characterizes statistically significant topology-function relationships in a given species, and (ii) uncovers the functions that have conserved topology in PINs of different species, which we term topologically orthologous functions. We apply our framework to PINs of yeast and human, identifying seven biological process and two cellular component GO terms to be topologically orthologous for the two organisms.Availability and implementation: http://bio-nets.doc.ic.ac.uk/goCCA.zipContact: natasha@imperial.ac.ukSupplementary information: Supplementary data are available at Bioinformatics online.