Toward Measuring Network Aesthetics Based on Symmetry

In this exploratory paper, we discuss quantitative graph-theoretical measures of network aesthetics. Related work in this area has typically focused on geometrical features (e.g., line crossings or edge bendiness) of drawings or visual representations of graphs which purportedly affect an observer’s perception. Here we take a very different approach, abandoning reliance on geometrical properties, and apply information-theoretic measures to abstract graphs and networks directly (rather than to their visual representaions) as a means of capturing classical appreciation of structural symmetry. Examples are used solely to motivate the approach to measurement, and to elucidate our symmetry-based mathematical theory of network aesthetics

Integrative Network Biology: Graph Prototyping for Co-Expression Cancer Networks

Network-based analysis has been proven useful in biologically-oriented areas, e.g., to explore the dynamics and complexity of biological networks. Investigating a set of networks allows deriving general knowledge about the underlying topological and functional properties. The integrative analysis of networks typically combines networks from different studies that investigate the same or similar research questions. In order to perform an integrative analysis it is often necessary to compare the properties of matching edges across the data set. This identification of common edges is often burdensome and computational intensive. Here, we present an approach that is different from inferring a new network based on common features. Instead, we select one network as a graph prototype, which then represents a set of comparable network objects, as it has the least average distance to all other networks in the same set. We demonstrate the usefulness of the graph prototyping approach on a set of prostate cancer networks and a set of corresponding benign networks. We further show that the distances within the cancer group and the benign group are statistically different depending on the utilized distance measure