Local Structures Determine Performance within Complex Networks

• Main Author: Krumov, Lachezar
• Format: Others
• Language: English; en
• Published: 2010
• Online Access: http://tuprints.ulb.tu-darmstadt.de/2321/2/WPM%242765.pdf; Krumov, Lachezar <http://tuprints.ulb.tu-darmstadt.de/view/person/Krumov=3ALachezar=3A=3A.html> : Local Structures Determine Performance within Complex Networks. Technische Universität, Darmstadt [Ph.D. Thesis], (2010)

Networks are ubiquitous. We as individuals are part of various social networks and each of us depends on multiple communication, traffic and supply networks in our everyday life. We are, however, still far from completely understanding and controlling those networks. Network motifs, few nodes (un)directed subgraphs, are a well-defined intermediate scale for characterizing the local structure of networks beyond the scope of single nodes. Motifs have so far been used only as a statistical measure. Their over- or under-representation in various networks has been related to specific topological function within those networks. This work investigates a so far unexplored perspective on complex networks. Namely, the relation between their motif content and the dynamic processes taking place on top of those networks. For this purpose, we project the dynamic output of a network back onto its topology and investigate weighted motifs while keeping the network topology intact. This approach is unique to this work and reveals a direct relation between the motif content and the output pattern of complex networks. We engage network motifs in two distinct ways. On the one side, as an analytical tool to examine already emerged networks. On the other side, as an active mechanism to adapt and improve human-made systems. A strong interplay is found between the local structures, the motif content, within a network and the dynamic performance of that network. Those new insights are used to develop a series of novel distributed topology control mechanisms. First, we use networks motifs as an analytical tool on a subclass of complex networks with large and easily accessible data sets: co-authorship networks. We address the question: Is there a relation between the citation frequencies of publications and the motifs they are involved in? Our analysis reveals a collaboration pattern much more successful than other collaboration patterns: the box motif, a closed chain of four authors. The box motif has the highest success measured as the average citation frequency per motif edge. Our findings are confirmed on two large data sets and on data snapshots over the past 20 years. Segregation seems to be the key to success: separation in time, rank and discipline are the major factors for the success of the box motif. An analytical generative model for co-authorship networks is introduced that can reproduce our findings and shreds light into the social factors shaping co-authorship networks. The revealed interplay between the motif content of complex networks and the dynamic processes taking place on those networks motivates a new perspective on distributed communication networks. We address the question: Instead to use network motifs just as a static analytical tool, is it possible to engage them in online decision rules to improve human-made systems? As a result we develop a novel topology control approach for Peer-to-Peer (P2P) networks. Each peer steers its local motif content to a desired state. Consequently, the overall network properties of the P2P overlay shifts towards a desired property. Fair load balancing in the demonstrated cases. Our evaluation shows that the new approach highly improves the network while causing negligible messaging overhead. Motivated by our results, we address a more general question: Are network motifs indeed also suitable for topology control within heterogeneous networks, where nodes play different roles? We extend our distributed topology control mechanism to heterogeneous P2P overlays. A novel approach for constructing highly resilient P2P live streaming networks is introduced. The peers choose from a set of rules how to adapt their motif content. The new approach induces resilience comparable to the state of the art methods. However, the topology of the constructed networks is better balanced than those of existing methods, making the new approach better performant under normal circumstances. Most importantly, the new approach requires no network knowledge. Consequently, the new method is not only much faster, but it also provides much higher privacy to the participating peers. Attacks by malicious parties are practically impossible. No peer can determine neither its position, nor the position of any other peer within the network. In that sense, the new proposed approach clearly outperforms the state of the art. Our findings so far clearly show that one can understand or even actively change the dynamic performance of networks by looking at their local topology. It is natural to investigate the opposite perspective: Is it possible to deploy suitable dynamic processes on a network with no global network knowledge, in order to reveal its topology? Consequently, we impose a dynamic process on top of a network in order to determine critical topological constellations within the network. By deploying an extended gossiping protocol, we show how one can detect communication bottlenecks in distributed manner. Our novel approach clearly outperforms state of the art methods with respect to both, the precision of its results and its performance. Last but no least, it has a guarding mechanism against malicious peers trying to skew the network protocol. So far we have shown that specific local structures lead to specific network properties and performance. Finally, we argue that random graphs and their random local structures also have unexploited potential. They have become notorious in the recent years for being poor null models of real world networks. Nevertheless, they have topological properties highly desirable within any P2P overlay. We introduce a novel P2P overlay based on random graphs. This new overlay is the first one to support exhaustive search queries and exact key-value lookups within the same overlay. Our overlay is both, highly scalable and efficient, and performs at least as good as already established P2P overlays. Throughout this work we repeatedly show that analyzing networks on intermediate scale opens so far unexplored and very fruitful perspectives on complex networks. The introduced new methodology for distributed topology control, advocated through this work, is just one of those perspectives.