Beyond Node Degree: Evaluating AS Topology Models

Topological relationship is one of the most basic and the most important relations between two spatial objects in GIS.However,current topological models have deficiencies when they are used to describe detailed topological relations.In this paper,one general descriptive form of topological relation model was proposed based on the node degree and the euler-number aiming at random two objects.In this model,all parts of one spatial object were treated as a whole object,and intersection difference operators were selected from several set operators to distinguish the topological relations,and four types of topological invariants were used for the computational results of contents,dimension,node degree,and euler-number.The topological description form of line-line,line-area,area-area were discussed emphatically.

The valley-free rule defines patterns of routing paths that allow the Internet Autonomous Systems (AS) to minimize their routing costs through selective announcement of BGP routes. The valley-free rule has been widely perceived as a universal property of the Internet BGP routing that is only violated due to transient configuration errors. Analysing the valley-free violations is important for a better understanding of BGP behaviour and inter-domain routing. This requires knowledge of the business relationships between ASes. The ground-truth data of AS relationships are not publicly available. Previous algorithms have inferred AS relationships based on the assumption that AS paths should be valley-free. Such inference results are biased and can not provide an objective assessment of the valley-free rule. Instead we extract the AS relationships directly from routing polices encoded in the BGP Community attribute. We are able to extract the business relationship of more than 30% of AS links based on BGP data collected from the RouteViews and RIPE RIS repositories in June 2011. We use our inferred AS relationships to analyse the valley-free violations in BGP routing. We reveal that the non valley-free paths are significantly more frequent than previously reported. As many as one fifth of AS paths in IPv6 BGP updates are valley paths. A substantial portion of these valley paths are persistent during the whole month of measurement. These observations strongly indicate that the valley paths are not merely a result of BGP misconfigurations. Instead they are the outcome of complex business relationships and deliberate policies by ASes using distinct unconventional models.

C. Faloutsos et al. (see Proc. ACM SIGCOMM, 1999) found that the inter autonomous system (AS) topology exhibits a power-law vertex degree distribution. This result was quite unexpected in the networking community and stirred significant interest in exploring the possible causes of this phenomenon. The work of A.-L. Barabasi and R. Albert (see Science, p.509-512, 1999) and its application to network topology generation in the work of A. Medina et al. (see Proc. MASCOTS, 2001) have explored a promising class of models that yield strict power-law vertex degree distributions. We re-examine the BGP (border gateway protocol) measurements that form the basis for the results reported by Faloutsos et al. We find that by their very nature (i.e., being strictly BGP-based), the data provides a very incomplete picture of Internet connectivity at the AS level. The AS connectivity maps constructed from this data (original maps) typically miss 20-50% or even more of the physical links in AS maps constructed using additional sources (extended maps). Subsequently, we find that while the vertex degree distributions resulting from the extended maps are heavy-tailed, they deviate significantly from a strict power law. Finally, we show that available historical data does not support the connectivity-based dynamics assumed by Barabasi and Albert. Together, our results suggest that the Internet topology at the AS level may well have developed over time following a very different set of growth processes than those proposed by Barabasi and Albert.

Representing the Internet as a succinct forest

Phase changes in the evolution of the IPv4 and IPv6 AS-Level Internet topologies

The Internet not only facilitates our daily activities, such as communication, entertainment and shopping but also serves as the enabling technology for many critical services, including finance, manufacturing, healthcare and transportation. On the other hand, a wide spectrum of attacks targets its communication infrastructure to disable or disrupt the network connectivity and traffic flow until recovery processes take place. Attacking all autonomous systems (ASes) in the Internet is typically beyond the capability of an adversary. Therefore, targeting a small number of ASes which results in the highest impact is the best strategy for attackers. Similarly, it is important for network practitioners to identify, fortify and secure those critical ASes to mitigate the impact of the attacks. In this study we introduce an intuitive and effective measure, IP address spatial path stress centrality, to assess and identify the critical ASes in the Internet. We compare IP address spatial path stress centrality to the three well-known and widely used centrality measures, namely customer-cone size, node degree and betweenness. We demonstrate that the proposed measure incorporates business relations and IP address spaces to achieve a better measure for identifying the critical ASes in the Internet.

Models for network topology form a crucial component in the analysis of protocols. This paper systematically investigates a variety of evolutionary models for autonomous system (AS) level Internet topology. Evolution-based models produce a topology incrementally, attempting to reflect the growth patterns of the actual topology. While evolutionary models are appealing, they have generally not agreed as closely with measurements of real data as non-evolutionary models. We attempt to understand what factor contributes to a "good" evolutionary model. Our systematic study consists of a relatively generic evolutionary model framework, which we populate with different choices for the components. This allows us to compare a variety of instances of models to measurements from real data sets. We study issues such as the initial topology, the type of preferential connectivity used when adding edges, and the role of "growth" edges added between existing nodes. We find that appropriate instantiation of the framework can provide topologies that agree closely with real data. We also use our work to highlight several crucial open problems in topology modeling.

Extracting a set of well connected subgraphs as communities from the Internet Autonomous System (AS) level topology graph is crucially important for a better understanding of the network structure and for designing new protocols. A huge number of community extraction methods have been proposed in the literature. In this paper we apply the k-dense algorithm as it represents a very interesting compromise between computational efficiency and precision. The paper provides two innovative contributions. The first is the application of the k-dense method to the Internet AS-level topology graph - obtained from the CAIDA, DIMES and IRL datasets - to identify well-connected communities and to analyze how these are connected to the rest of the graph. The second contribution relates to the study of the most well-connected communities with the support of two additional datasets: a geographical dataset (which lists, for each AS, the countries in which it has at least one geographical location) and the Internet eXchange Point dataset (which maintains, for each IXP, its geographical position and the list of its participants). We found that the k-max-dense community holds a central position in the Internet AS-level topology graph structure since its 101 ASes (less than the 0.3% of Internet ASes) are involved in more than 39% of all Internet connections. We also found that those ASes are connected to at least one IXP and have at least one geographical location in Europe (only 70.3% of them have at least one additional geographical location outside Europe).

Denial of service (DoS) attack on the Internet has become a pressing problem. In this paper, we describe and evaluate route-based distributed packet filtering (DPF), a novel approach to distributed DoS (DDoS) attack prevention. We show that DPF achieves proactiveness and scalability, and we show that there is an intimate relationship between the effectiveness of DPF at mitigating DDoS attack and power-law network topology.The salient features of this work are two-fold. First, we show that DPF is able to proactively filter out a significant fraction of spoofed packet flows and prevent attack packets from reaching their targets in the first place. The IP flows that cannot be proactively curtailed are extremely sparse so that their origin can be localized---i.e., IP traceback---to within a small, constant number of candidate sites. We show that the two proactive and reactive performance effects can be achieved by implementing route-based filtering on less than 20% of Internet autonomous system (AS) sites. Second, we show that the two complementary performance measures are dependent on the properties of the underlying AS graph. In particular, we show that the power-law structure of Internet AS topology leads to connectivity properties which are crucial in facilitating the observed performance effects.

Attacks launched over the Internet have become a pressing problem. Attackers make use of a variety of techniques to anonymize their traffic, in order to escape detection and prosecution. Despite much research on attack attribution, there has been little work on optimizing the number and placement of monitoring points for identifying the source of attacks with minimum ambiguity. This paper proposes such a method. The approach is based on the concept of graph separators. A separator partitions a network, such that the size of the separator is the number of monitors needed, and the size of a partition is the ambiguity in isolating the specific source of an attack. To achieve a desired degree of ambiguity, a good separator for the Internet is sought. Both vertex and edge separator heuristics are presented, which greedily select vertices of highest/lowest degree as monitors. The methods are evaluated for the Internet autonomous system (AS) topology. Experimental results show that the vertex separator heuristic requires just 5% of the ASes to be monitored to identify the source of an attack with little ambiguity. If only those links actually used for routing to a specific destination are considered, use of an edge separator requires 30% of the links to be monitored to achieve similar results. The results can be further improved if it is known that ASes have unequal probabilities of being the source of an attack.

In this work, we employed the concept of the first-passage time in stochastic processes to estimate node degrees and the degree distribution of a network. A statistical exploration of the coupling reveals the relation between the node degree and the coupling term. In practical terms, an effective way to reveal the statistical property is to investigate the differences between coupled oscillators in a network and uncoupled ones with the same initial states. We discovered a monotonically decreasing relation between the node degree and the mean first-passage time (MFPT) for the evolution of the coupled node deviating from the uncoupled one. Moreover, this relation can be understood as the competition of different relaxational time scales. The MFPT method is independent of both the dynamics of the nodes and the topological properties of the network. This might be advantageous in our efforts to build a bridge between the topological property and the dynamics of a network.

Signal flow direction is one of the most important features of the protein-protein interactions in signaling networks. However, almost all the outcomes of current high-throughout techniques for protein-protein interactions mapping are usually supposed to be non-directional. Based on the pairwise interaction domains, here we defined a novel parameter protein interaction directional score and then used it to predict the direction of signal flow between proteins in proteome-wide signaling networks. Using 5-fold cross-validation, our approach obtained a satisfied performance with the accuracy 89.79%, coverage 48.08%, and error ratio 16.91%. As an application, we established an integrated human directional protein interaction network, including 2,237 proteins and 5,530 interactions, and inferred a large amount of novel signaling pathways. Directional protein interaction network was strongly supported by the known signaling pathways literature (with the 87.5% accuracy) and further analyses on the biological annotation, subcellular localization, and network topology property. Thus, this study provided an effective method to define the upstream/downstream relations of interacting protein pairs and a powerful tool to unravel the unknown signaling pathways.

Structure information plays an important role in both object recognition and detection. This paper studies what visual structure is and addresses the problem of structure modeling and representation from two aspects: visual feature and topology model. Firstly, at feature level, we propose Local Structured Descriptor to capture the object’s local structure effectively, and develop the descriptors from shape and texture information, respectively. Secondly, at topology level, we present a local structured model with a boosted feature selection and fusion scheme. All experiments are conducted on the challenging PASCAL Visual Object Classes (VOC) datasets from VOC2007 to VOC2010. Experimental results show that our method achieves very competitive performance.

Internet Service Providers (ISPs) have different growth or decline patterns in terms of topological and economic characteristics. While some ISPs may have a significant correlation between their topological and business properties, others may not show such strong techno-economic dependence. In this paper, we examine the relationship between the network topology characteristics of the ISPs and their stock market values. We analyze data collected from two different datasets of inter-ISP relationships of various types, i.e., customer, provider and peer. Then, we correlate these topological relationships against the ISPs performance on the stock market. In particular, we examine the correlation between the stock market values as well as revenue of each major ISPs operating in the United States to their degree (i.e., the number of connections they have to other Autonomous Systems) and customer cone size (i.e., the number of customers they are serving).

In this work, we systematically analyzed the effects of various nodal definitions, as determined by a multi-granularity whole-brain segmentation scheme, upon the topological architecture of the human brain functional network using the resting-state functional magnetic resonance imaging data of 19 healthy, young subjects. A number of functional networks were created with their nodes defined according to two types of anatomical definitions (Type I and Type II) each of which consists of five granularity levels of whole brain segmentations with each level linked through ontology-based, hierarchical, structural relationships. Topological properties were computed for each network and then compared across levels within the same segmentation type as well as between Type I and Type II. Certain network architecture patterns were observed in our study: (1) As the granularity changes, the absolute values of each node's nodal degree and nodal betweenness change accordingly but the relative values within a single network do not change considerably; (2) The average nodal degree is generally affected by the sparsity level of the network whereas the other topological properties are more specifically affected by the nodal definitions; (3) Within the same ontology relationship type, as the granularity decreases, the network becomes more efficient at information propagation; (4) The small-worldness that we observe is an intrinsic property of the brain's resting-state functional network, independent of the ontology type and the granularity level. Furthermore, we validated the aforementioned conclusions and measured the reproducibility of this multi-granularity network analysis pipeline using another dataset of 49 healthy young subjects that had been scanned twice.