Core-periphery organization of complex networks

Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy. We measure this coefficient for a number of real-world and model networks and find that different classes of networks have their characteristic values. For example do geographical networks have a strong core-periphery structure, while the core-periphery structure of social networks (despite their positive degree-degree correlations) is rather weak. We proceed to study radial statistics of the core, i.e. properties of the n-neighborhoods of the core vertices for increasing n. We find that almost all networks have unexpectedly many edges within n-neighborhoods at a certain distance from the core suggesting an effective radius for non-trivial network processes

Hierarchy Measures in Complex Networks

Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally hierarchical. Comparison with these extremal cases as well as with random scale-free networks allows us to better understand hierarchical versus modular features in several real-life complex networks. For random scale-free topologies the extent of topological hierarchy is shown to smoothly decline with $\gamma$ -- the exponent of a degree distribution -- reaching its highest possible value for $\gamma \leq 2$ and quickly approaching zero for $\gamma>3$.Comment: 4 pages, 4 figure

Popular Cultural Keystone Species are also understudied — the case of the camphor tree (Dryobalanops aromatica)

Along with landscape degradation and loss of biodiversity there is also a co-occurring loss of cultural and linguistic diversity. When species become rare, there is a corresponding loss of cultural practices and linguistic elements associated with that species. Although cultural assessments of tree species can help in identifying Cultural Keystone Species (CKS) and be used to enhance the cultural relevance of conservation actions, such information is typically lacking for endangered species were the cultural connections may have been lost. Here, we review historic written accounts to assess the cultural status of the critically endangered camphor tree, Dryobalanops aromatica, native to Southeast Asia which is recognized for its camphor and crystals forming in the wood. We found that despite centuries of use, the importance of the tree for specific cultures has not been fully understood. Published literature indicate that it could be a CKS to multiple communities. The tree was once culturally significant for many cultures in its native range and beyond, but contemporary data is lacking, especially with respect to persistence and memory of use in relation to cultural change. By virtue of being a culturally recognized tree species, as well as having a distinct ecological role within its natural distribution, we propose D. aromatica as a flagship species for conservation and restoration of the habitat it defines. Our review highlights the usability of historic accounts as starting points for identifying CKS and effective conservation of biocultural diversity, especially concerning endangered species. We propose that future research should pay attention to inter and intra-community dynamics of local knowledge on the species, and causes and consequences of varying cultural importance across temporal and spatial scale

Nonequilibrium phase transition in the coevolution of networks and opinions

Models of the convergence of opinion in social systems have been the subject of a considerable amount of recent attention in the physics literature. These models divide into two classes, those in which individuals form their beliefs based on the opinions of their neighbors in a social network of personal acquaintances, and those in which, conversely, network connections form between individuals of similar beliefs. While both of these processes can give rise to realistic levels of agreement between acquaintances, practical experience suggests that opinion formation in the real world is not a result of one process or the other, but a combination of the two. Here we present a simple model of this combination, with a single parameter controlling the balance of the two processes. We find that the model undergoes a continuous phase transition as this parameter is varied, from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion. We characterize the static and dynamical properties of this transition