A New Method for Assessing the Resiliency of Large, Complex Networks

Designing resilient and reliable networks is a principle concern of planners and private firms. Traffic congestion whether recurring or as the result of some aperiodic event is extremely costly. This paper describes an alternative process and a model for analyzing the resiliency of networks that address some of the shortcomings of more traditional approaches – e.g., the four-step modeling process used in transportation planning. It should be noted that the authors do not view this as a replacement to current approaches but rather as a complementary tool designed to augment analysis capabilities. The process that is described in this paper for analyzing the resiliency of a network involves at least three steps: 1. assessment or identification of important nodes and links according to different criteria 2. verification of critical nodes and links based on failure simulations and 3. consequence. Raster analysis, graph-theory principles and GIS are used to develop a model for carrying out each of these steps. The methods are demonstrated using two, large interdependent networks for a metropolitan area in the United States.

The brainstem reticular formation is a small-world, not scale-free, network

Recently, it has been demonstrated that several complex systems may have simple graph-theoretic characterizations as so-called ‘small-world’ and ‘scale-free’ networks. These networks have also been applied to the gross neural connectivity between primate cortical areas and the nervous system of Caenorhabditis elegans. Here, we extend this work to a specific neural circuit of the vertebrate brain—the medial reticular formation (RF) of the brainstem—and, in doing so, we have made three key contributions. First, this work constitutes the first model (and quantitative review) of this important brain structure for over three decades. Second, we have developed the first graph-theoretic analysis of vertebrate brain connectivity at the neural network level. Third, we propose simple metrics to quantitatively assess the extent to which the networks studied are small-world or scale-free. We conclude that the medial RF is configured to create small-world (implying coherent rapid-processing capabilities), but not scale-free, type networks under assumptions which are amenable to quantitative measurement

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

A Graph Theoretic Perspective on Internet Topology Mapping

Understanding the topological characteristics of the Internet is an important research issue as the Internet grows with no central authority. Internet topology mapping studies help better understand the structure and dynamics of the Internet backbone. Knowing the underlying topology, researchers can better develop new protocols and services or fine-tune existing ones. Subnet-level Internet topology measurement studies involve three stages: topology collection, topology construction, and topology analysis. Each of these stages contains challenging tasks, especially when large-scale backbone topologies of millions of nodes are studied. In this dissertation, I first discuss issues in subnet-level Internet topology mapping and review state-of-the-art approaches to handle them. I propose a novel graph data indexing approach to to efficiently process large scale topology data. I then conduct an experimental study to understand how the responsiveness of routers has changed over the last decade and how it differs based on the probing mechanism. I then propose an efficient unresponsive resolution approach by incorporating our structural graph indexing technique. Finally, I introduce Cheleby, an integrated Internet topology mapping system. Cheleby first dynamically probes observed subnetworks using a team of PlanetLab nodes around the world to obtain comprehensive backbone topologies. Then, it utilizes efficient algorithms to resolve subnets, IP aliases, and unresponsive routers in the collected data sets to construct comprehensive subnet-level topologies. Sample topologies are provided at http://cheleby.cse.unr.edu