Intrinsically Dynamic Network Communities

Community finding algorithms for networks have recently been extended to dynamic data. Most of these recent methods aim at exhibiting community partitions from successive graph snapshots and thereafter connecting or smoothing these partitions using clever time-dependent features and sampling techniques. These approaches are nonetheless achieving longitudinal rather than dynamic community detection. We assume that communities are fundamentally defined by the repetition of interactions among a set of nodes over time. According to this definition, analyzing the data by considering successive snapshots induces a significant loss of information: we suggest that it blurs essentially dynamic phenomena - such as communities based on repeated inter-temporal interactions, nodes switching from a community to another across time, or the possibility that a community survives while its members are being integrally replaced over a longer time period. We propose a formalism which aims at tackling this issue in the context of time-directed datasets (such as citation networks), and present several illustrations on both empirical and synthetic dynamic networks. We eventually introduce intrinsically dynamic metrics to qualify temporal community structure and emphasize their possible role as an estimator of the quality of the community detection - taking into account the fact that various empirical contexts may call for distinct `community' definitions and detection criteria.Comment: 27 pages, 11 figure

Emergence of (bi)multi-partiteness in networks having inhibitory and excitatory couplings

(Bi)multi-partite interaction patterns are commonly observed in real world systems which have inhibitory and excitatory couplings. We hypothesize these structural interaction pattern to be stable and naturally arising in the course of evolution. We demonstrate that a random structure evolves to the (bi)multi-partite structure by imposing stability criterion through minimization of the largest eigenvalue in the genetic algorithm devised on the interacting units having inhibitory and excitatory couplings. The evolved interaction patterns are robust against changes in the initial network architecture as well as fluctuations in the interaction weights.Comment: 6 pages, 7 figure

Beyond similarity: A network approach for identifying and delimiting biogeographical regions

Biogeographical regions (geographically distinct assemblages of species and communities) constitute a cornerstone for ecology, biogeography, evolution and conservation biology. Species turnover measures are often used to quantify biodiversity patterns, but algorithms based on similarity and clustering are highly sensitive to common biases and intricacies of species distribution data. Here we apply a community detection approach from network theory that incorporates complex, higher order presence-absence patterns. We demonstrate the performance of the method by applying it to all amphibian species in the world (c. 6,100 species), all vascular plant species of the USA (c. 17,600), and a hypothetical dataset containing a zone of biotic transition. In comparison with current methods, our approach tackles the challenges posed by transition zones and succeeds in identifying a larger number of commonly recognised biogeographical regions. This method constitutes an important advance towards objective, data derived identification and delimitation of the world's biogeographical regions.Comment: 5 figures and 1 supporting figur