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Register a new userCharacterizing the Robustness of Complex Networks
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Added by
Ali Sydney
Publication date
2009
fields
Informatics Engineering
and research's language is
English
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With increasingly ambitious initiatives such as GENI and FIND that seek to design the future Internet, it becomes imperative to define the characteristics of robust topologies, and build future networks optimized for robustness. This paper investigates the characteristics of network topologies that maintain a high level of throughput in spite of multiple attacks. To this end, we select network topologies belonging to the main network models and some real world networks. We consider three types of attacks: removal of random nodes, high degree nodes, and high betweenness nodes. We use elasticity as our robustness measure and, through our analysis, illustrate that different topologies can have different degrees of robustness. In particular, elasticity can fall as low as 0.8% of the upper bound based on the attack employed. This result substantiates the need for optimized network topology design. Furthermore, we implement a tradeoff function that combines elasticity under the three attack strategies and considers the cost of the network. Our extensive simulations show that, for a given network density, regular and semi-regular topologies can have higher degrees of robustness than heterogeneous topologies, and that link redundancy is a sufficient but not necessary condition for robustness.
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Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex networks defines the resolve of a network to maintain functionality in the advent of classical component failures and at the onset of cryptic malicious attacks. To date, robustness metrics are deficient and unfortunately the following dilemmas exist: accurate models necessitate complex analysis while conversely, simple models lack applicability to our definition of robustness. In this paper, we define robustness and present a novel metric, elasticity- a bridge between accuracy and complexity-a link in the chain of network robustness. Additionally, we explore the performance of elasticity on Internet topologies and online social networks, and articulate results.
The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in such a graph possess some non-trivial internal structure that varies across and differentiates among distinct types of links or nodes. In this work, we abstract such additional information as network annotations. We introduce a network topology modeling framework that treats annotations as an extended correlation profile of a network. Assuming we have this profile measured for a given network, we present an algorithm to rescale it in order to construct networks of varying size that still reproduce the original measured annotation profile. Using this methodology, we accurately capture the network properties essential for realistic simulations of network applications and protocols, or any other simulations involving complex network topologies, including modeling and simulation of network evolution. We apply our approach to the Autonomous System (AS) topology of the Internet annotated with business relationships between ASs. This topology captures the large-scale structure of the Internet. In depth understanding of this structure and tools to model it are cornerstones of research on future Internet architectures and designs. We find that our techniques are able to accurately capture the structure of annotation correlations within this topology, thus reproducing a number of its important properties in synthetically-generated random graphs.
This work started out with our accidental discovery of a pattern of throughput distributions among links in IEEE 802.11 networks from experimental results. This pattern gives rise to an easy computation method, which we term back-of-the-envelop (BoE) computation, because for many network configurations, very accurate results can be obtained within minutes, if not seconds, by simple hand computation. BoE beats prior methods in terms of both speed and accuracy. While the computation procedure of BoE is simple, explaining why it works is by no means trivial. Indeed the majority of our investigative efforts have been devoted to the construction of a theory to explain BoE. This paper models an ideal CSMA network as a set of interacting on-off telegraph processes. In developing the theory, we discovered a number of analytical techniques and observations that have eluded prior research, such as that the carrier-sensing interactions among links in an ideal CSMA network result in a system state evolution that is time-reversible; and that the probability distribution of the system state is insensitive to the distributions of the on and off durations given their means, and is a Markov random field. We believe these theoretical frameworks are useful not just for explaining BoE, but could also be a foundation for a fundamental understanding of how links in CSMA networks interact. Last but not least, because of their basic nature, we surmise that some of the techniques and results developed in this paper may be applicable to not just CSMA networks, but also to other physical and engineering systems consisting of entities interacting with each other in time and space.
In the course of the growth of the Internet and due to increasing availability of data, over the last two decades, the field of network science has established itself as an own area of research. With quantitative scientists from computer science, mathematics, and physics working on datasets from biology, economics, sociology, political sciences, and many others, network science serves as a paradigm for interdisciplinary research. One of the major goals in network science is to unravel the relationship between topological graph structure and a networks function. As evidence suggests, systems from the same fields, i.e. with similar function, tend to exhibit similar structure. However, it is still vague whether a similar graph structure automatically implies likewise function. This dissertation aims at helping to bridge this gap, while particularly focusing on the role of triadic structures. After a general introduction to the main concepts of network science, existing work devoted to the relevance of triadic substructures is reviewed. A major challenge in modeling such structure is the fact that not all three-node subgraphs can be specified independently of each other, as pairs of nodes may participate in multiple triadic subgraphs. In order to overcome this obstacle, a novel class of generative network models based on pair-disjoint triadic building blocks is suggested. It is further investigated whether triad motifs - subgraph patterns which appear significantly more frequently than expected at random - occur homogeneously or heterogeneously distributed over graphs. Finally, the influence of triadic substructure on the evolution of dynamical processes acting on their nodes is studied. It is observed that certain motifs impose clear signatures on the systems dynamics, even when embedded in a larger network structure.
This paper has been withdrawn by the authors.
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