Experiments on comparing graph clusterins

A promising approach to compare graph clusterings is based on using measurements for calculating the distance. Existing measures either use the structure of clusterings or quality--based aspects. Each approach suffers from critical drawbacks. We introduce a new approach combining both aspects and leading to better results for comparing graph clusterings. An experimental evaluation of existing and new measures shows that the significant drawbacks of existing techniques are not only theoretical in nature and proves that the results of our new measures are more coherent with intuition

A new paradigm for complex network visualization

We propose a new layout paradigm for drawing a nested decomposition of a large network. The visualization supports the recognition of abstract features of the decomposition, while drawing all elements. In order to support the visual analysis that focuses on the dependencies of the individual parts of the decomposition, we use an annulus as the general underlying shape. This method has been evaluated using real world data and offers surprising readability

Analysis of the autonomous system network and of overlay networks using visualization

Taking the physical Internet at the Autonomous System (AS) level as an instance of a complex network, and Gnutella as a popular peer-to-peer application running on top of it, we investigated the correlation of overlay networks with their underlying topology using visualization. We find that while overlay networks create arbitrary topologies, they differ from randomly generated networks, and there is a correlation with the underlying network. In addition, we successfully validated the applicability of our visualization technique for AS topologies by comparing Routeviews data sets with DIMES data sets, and by analyzing the temporal evolution in the Routeviews data sets

On Modularity - NP-Completeness and Beyond

Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, and in particular in the complex systems literature, although its properties are not well understood. We here present first results on the computational and analytical properties of modularity. The complexity status of modularity maximization is resolved showing that the corresponding decision version is NP-complete in the strong sense. We also give a formulation as an Integer Linear Program (ILP) to facilitate exact optimization, and provide results on the approximation factor of the commonly used greedy algorithm. Completing our investigation, we characterize clusterings with maximum Modularity for several graph families

Clustering with Spectral Methods

Grouping and sorting are problems with a great tradition in the history of mankind. Clustering and cluster analysis is a small aspect in the wide spectrum. But these topics have applications in most scientific disciplines. Graph clustering is again a little fragment in the clustering area. Nevertheless it has the potential for new pioneering and innovative methods. One such method is the Markov Clustering presented by van Dongen in 'Graph Clustering by Flow Simulation'. We investigated the question, if there is a similar approach which involves the graph structure more directly and has a linear space complexity

Maximum Rigid Components as Means for Direction-Based Localization in Sensor Networks

Many applications in sensor networks require positional information of the sensors. Recovering node positions is closely related to graph realization problems for geometric graphs. Here, we address the case where nodes have angular information. Whereas Bruck et al. proved that the corresponding realization problem together with unit-disk-graph-constraints is NP-hard [2], we focus on rigid components which allow both efficient identification and fast, unique realizations. Our technique allows to identify maximum rigid components in graphs with partially known rigid components using a reduction to maximum flow problems. This approach is analyzed for the two-dimensional case, but can easily be extended to higher dimensions

Dynamic analysis of the Autonomous System graph

In this paper we investigate to what extent the information provided by BGP routing tables about the graph of the Autonomous Systems (ASes) can be used to understand dynamic phenomena occurring in the network. First, we classify the time scales at which such an analysis can be performed and, consequently, the kinds of phenomena that could be anticipated. Second, we improve cutting-edge technologies used to analyze the structure of the network, most notably spectral methods for graph clustering, in order to be able to analyze a whole sequence of consecutive snapshots that capture the temporal evolution of the network. Finally, we use such tools to analyze the data collected by the Oregon RouteViews project [20] during the last few years. We confirm stable properties of the AS graph, find major trends and notice that events occurring on a smaller time-frame, like worm-attacks, misconfigurations, outages, DDoS attacks, etc. seem to have a very diverse degree of impact on the AS graph structure, which suggests that these techniques could be used to distinguish some of them.

Dynamic Analysis of the Autonomous System Graph

In this paper we investigate to what extent the information provided by BGP routing tables about the graph of the Autonomous Systems (ASes) can be used to understand dynamic phenomena occurring in the network. First, we classify the time scales at which such an analysis can be performed and, consequently, the kinds of phenomena that could be anticipated. Second, we improve cutting-edge technologies used to analyze the structure of the network, most notably spectral methods for graph clustering, in order to be able to analyze a whole sequence of consecutive snapshots that capture the temporal evolution of the network. Finally, we use such tools to analyze the data collected by the Oregon RouteViews project [20] during the last few years. We confirm stable properties of the AS graph, find major trends and notice that events occurring on a smaller time-frame, like worm-attacks, misconfigurations, outages, DDoS attacks, etc. seem to have a very diverse degree of impact on the AS graph structure, which suggests that these techniques could be used to distinguish some of them.

A hybrid model for drawing dynamic and evolving graphs

Abstract. Dynamic processes frequently occur in many applications. Visualizations of dynamically evolving data, for example as part of the data analysis, are typically restricted to a cumulative static view or an animation/sequential view. Both methods have their benefits and are often complementary in their use. In this article, we present a hybrid model that combines the two techniques. This is accomplished by 2.5D drawings which are calculated in an incremental way. The method has been evaluated on collaboration networks.