Complex Networks from Simple Rewrite Systems

Complex networks are all around us, and they can be generated by simple mechanisms. Understanding what kinds of networks can be produced by following simple rules is therefore of great importance. We investigate this issue by studying the dynamics of extremely simple systems where are `writer' moves around a network, and modifies it in a way that depends upon the writer's surroundings. Each vertex in the network has three edges incident upon it, which are colored red, blue and green. This edge coloring is done to provide a way for the writer to orient its movement. We explore the dynamics of a space of 3888 of these `colored trinet automata' systems. We find a large variety of behaviour, ranging from the very simple to the very complex. We also discover simple rules that generate forms which are remarkably similar to a wide range of natural objects. We study our systems using simulations (with appropriate visualization techniques) and analyze selected rules mathematically. We arrive at an empirical classification scheme which reveals a lot about the kinds of dynamics and networks that can be generated by these systems

The Regularizing Capacity of Metabolic Networks

Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from steady states. This leads to the interesting question, how metabolic networks avoid complex dynamics and maintain a steady-state behavior. Here, we expose metabolic network topologies to binary dynamics generated by simple local rules. We find that the networks' response is highly specific: Complex dynamics are systematically reduced on metabolic networks compared to randomized networks with identical degree sequences. Already small topological modifications substantially enhance the capacity of a network to host complex dynamic behavior and thus reduce its regularizing potential. This exceptionally pronounced regularization of dynamics encoded in the topology may explain, why steady-state behavior is ubiquitous in metabolism.Comment: 6 pages, 4 figure

Complex networks as an emerging property of hierarchical preferential attachment

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.Comment: 12 pages, 7 figure

Symbolic dynamics of biological feedback networks

We formulate general rules for a coarse-graining of the dynamics, which we term `symbolic dynamics', of feedback networks with monotone interactions, such as most biological modules. Networks which are more complex than simple cyclic structures can exhibit multiple different symbolic dynamics. Nevertheless, we show several examples where the symbolic dynamics is dominated by a single pattern that is very robust to changes in parameters and is consistent with the dynamics being dictated by a single feedback loop. Our analysis provides a method for extracting these dominant loops from short time series, even if they only show transient trajectories.Comment: 4 pages, 4 figure

Self-organization of Nodes using Bio-Inspired Techniques for Achieving Small World Properties

In an autonomous wireless sensor network, self-organization of the nodes is essential to achieve network wide characteristics. We believe that connectivity in wireless autonomous networks can be increased and overall average path length can be reduced by using beamforming and bio-inspired algorithms. Recent works on the use of beamforming in wireless networks mostly assume the knowledge of the network in aggregation to either heterogeneous or hybrid deployment. We propose that without the global knowledge or the introduction of any special feature, the average path length can be reduced with the help of inspirations from the nature and simple interactions between neighboring nodes. Our algorithm also reduces the number of disconnected components within the network. Our results show that reduction in the average path length and the number of disconnected components can be achieved using very simple local rules and without the full network knowledge.Comment: Accepted to Joint workshop on complex networks and pervasive group communication (CCNet/PerGroup), in conjunction with IEEE Globecom 201