Exploring Statistical and Population Aspects of Network Complexity

The characterization and the definition of the complexity of objects is an important but very difficult problem that attracted much interest in many different fields. In this paper we introduce a new measure, called network diversity score (NDS), which allows us to quantify structural properties of networks. We demonstrate numerically that our diversity score is capable of distinguishing ordered, random and complex networks from each other and, hence, allowing us to categorize networks with respect to their structural complexity. We study 16 additional network complexity measures and find that none of these measures has similar good categorization capabilities. In contrast to many other measures suggested so far aiming for a characterization of the structural complexity of networks, our score is different for a variety of reasons. First, our score is multiplicatively composed of four individual scores, each assessing different structural properties of a network. That means our composite score reflects the structural diversity of a network. Second, our score is defined for a population of networks instead of individual networks. We will show that this removes an unwanted ambiguity, inherently present in measures that are based on single networks. In order to apply our measure practically, we provide a statistical estimator for the diversity score, which is based on a finite number of samples

Geocentrism vs genocentrism: theories without metaphors, metaphors without theories

International audienceThrough the comparison between two major, long-lasting theoretical frameworks-geocentrism and genocentrism-we discuss the different epistemological role played by metaphors in physics and biology. Throughout its history, physics developed theories and mathematical formalisms, which either do not seem to rely on metaphors at all (as geocentrism) or have absorbed initial thrusting metaphors into original theoretical frameworks. When considering genocentrism, in turn, the situation looks different. For some authors, genocentric theories are not metaphorical, but for opposite reasons with respect to geocentrism: pivotal concepts of information theories are straightforwardly imported as theoretical ones into biology. For others, the reference to information in genocentrism is indeed metaphorical, although the similarities and dissimilarities are not spelt out. Some problematic consequences of the application of genocentrism to biology are discussed