Degree landscapes in scale-free networks

Community landscapes: an integrative approach to determine overlapping network module hierarchy, identify key nodes and predict network dynamics

Background

Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult.

Methodology/Principal Findings

Here we introduce the novel concept of ModuLand, an integrative method family determining overlapping network modules as hills of an influence function-based, centrality-type community landscape, and including several widely used modularization methods as special cases. As various adaptations of the method family, we developed several algorithms, which provide an efficient analysis of weighted and directed networks, and (1) determine pervasively overlapping modules with high resolution; (2) uncover a detailed hierarchical network structure allowing an efficient, zoom-in analysis of large networks; (3) allow the determination of key network nodes and (4) help to predict network dynamics.

Conclusions/Significance

The concept opens a wide range of possibilities to develop new approaches and applications including network routing, classification, comparison and prediction.

One hub-one process: a tool based view on regulatory network topology

Background

The relationship between the regulatory design and the functionality of molecular networks is a key issue in biology. Modules and motifs have been associated to various cellular processes, thereby providing anecdotal evidence for performance based localization on molecular networks.

Results

To quantify structure-function relationship we investigate similarities of proteins which are close in the regulatory network of the yeast Saccharomyces Cerevisiae. We find that the topology of the regulatory network only show weak remnants of its history of network reorganizations, but strong features of co-regulated proteins associated to similar tasks. These functional correlations decreases strongly when one consider proteins separated by more than two steps in the regulatory network. The network topology primarily reflects the processes that is orchestrated by each individual hub, whereas there is nearly no remnants of the history of protein duplications.

Conclusion

Our results suggests that local topological features of regulatory networks, including broad degree distributions, emerge as an implicit result of matching a number of needed processes to a finite toolbox of proteins.

Exploring the assortativity-clustering space of a network's degree sequence

Nowadays there is a multitude of measures designed to capture different aspects of network structure. To be able to say if a measured value is expected or not, one needs to compare it with a reference model (null model). One frequently used null model is the ensemble of graphs with the same set of degrees as the original network. Here, we argue that this ensemble can give more information about the original network than effective values of network structural quantities. By mapping out this ensemble in the space of some low-level network structure--in our case, those measured by the assortativity and clustering coefficients--one can, for example, study where in the valid region of the parameter space the observed networks are. Such analysis suggests which quantities (or combination of quantities) are actively optimized during the evolution of the network. We use four very different biological networks to exemplify our method. Among other things, we find that high clustering might be a force in the evolution of protein interaction networks. We also find that all four networks are conspicuously robust to both random errors and targeted attacks.