Kronecker Graphs: An Approach to Modeling Networks

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and densification and shrinking diameters over time. Most present network models either fail to match several of the above properties, are complicated to analyze mathematically, or both. In this paper we propose a generative model for networks that is both mathematically tractable and can generate networks that have the above mentioned properties. Our main idea is to use the Kronecker product to generate graphs that we refer to as "Kronecker graphs". First, we prove that Kronecker graphs naturally obey common network properties. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KronFit, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super- exponential time. In contrast, KronFit takes linear time, by exploiting the structure of Kronecker matrix multiplication and by using statistical simulation techniques. Experiments on large real and synthetic networks show that KronFit finds accurate parameters that indeed very well mimic the properties of target networks. Once fitted, the model parameters can be used to gain insights about the network structure, and the resulting synthetic graphs can be used for null- models, anonymization, extrapolations, and graph summarization

Stochastic Analysis of a Churn-Tolerant Structured Peer-to-Peer Scheme

We present and analyze a simple and general scheme to build a churn (fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to "convert" a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p). Applying our scheme to a cube-connected cycles network, for example, yields a $O(\log N)$ degree connected network, in which every search succeeds in $O(\log N)$ hops w.h.p., using $O(\log N)$ messages, where $N$ is the expected stable network size. Our scheme has an constant storage overhead (the number of nodes responsible for servicing a data item) and an $O(\log N)$ overhead (messages and time) per insertion and essentially no overhead for deletions. All these bounds are essentially optimal. While DHT schemes with similar guarantees are already known in the literature, this work is new in the following aspects: (1) It presents a rigorous mathematical analysis of the scheme under a general stochastic model of churn and shows the above guarantees; (2) The theoretical analysis is complemented by a simulation-based analysis that validates the asymptotic bounds even in moderately sized networks and also studies performance under changing stable network size; (3) The presented scheme seems especially suitable for maintaining dynamic structures under churn efficiently. In particular, we show that a spanning tree of low diameter can be efficiently maintained in constant time and logarithmic number of messages per insertion or deletion w.h.p. Keywords: P2P Network, DHT Scheme, Churn, Dynamic Spanning Tree, Stochastic Analysis

Defending Tor from Network Adversaries: A Case Study of Network Path Prediction

The Tor anonymity network has been shown vulnerable to traffic analysis attacks by autonomous systems and Internet exchanges, which can observe different overlay hops belonging to the same circuit. We aim to determine whether network path prediction techniques provide an accurate picture of the threat from such adversaries, and whether they can be used to avoid this threat. We perform a measurement study by running traceroutes from Tor relays to destinations around the Internet. We use the data to evaluate the accuracy of the autonomous systems and Internet exchanges that are predicted to appear on the path using state-of-the-art path inference techniques; we also consider the impact that prediction errors have on Tor security, and whether it is possible to produce a useful overestimate that does not miss important threats. Finally, we evaluate the possibility of using these predictions to actively avoid AS and IX adversaries and the challenges this creates for the design of Tor

A complex network approach to urban growth

The economic geography can be viewed as a large and growing network of interacting activities. This fundamental network structure and the large size of such systems makes complex networks an attractive model for its analysis. In this paper we propose the use of complex networks for geographical modeling and demonstrate how such an application can be combined with a cellular model to produce output that is consistent with large scale regularities such as power laws and fractality. Complex networks can provide a stringent framework for growth dynamic modeling where concepts from e.g. spatial interaction models and multiplicative growth models can be combined with the flexible representation of land and behavior found in cellular automata and agent-based models. In addition, there exists a large body of theory for the analysis of complex networks that have direct applications for urban geographic problems. The intended use of such models is twofold: i) to address the problem of how the empirically observed hierarchical structure of settlements can be explained as a stationary property of a stochastic evolutionary process rather than as equilibrium points in a dynamics, and, ii) to improve the prediction quality of applied urban modeling.evolutionary economics, complex networks, urban growth

Content-access QoS in peer-to-peer networks using a fast MDS erasure code

This paper describes an enhancement of content access Quality of Service in peer to peer (P2P) networks. The main idea is to use an erasure code to distribute the information over the peers. This distribution increases the users’ choice on disseminated encoded data and therefore statistically enhances the overall throughput of the transfer. A performance evaluation based on an original model using the results of a measurement campaign of sequential and parallel downloads in a real P2P network over Internet is presented. Based on a bandwidth distribution, statistical content-access QoS are guaranteed in function of both the content replication level in the network and the file dissemination strategies. A simple application in the context of media streaming is proposed. Finally, the constraints on the erasure code related to the proposed system are analysed and a new fast MDS erasure code is proposed, implemented and evaluated

Mobility Study for Named Data Networking in Wireless Access Networks

Information centric networking (ICN) proposes to redesign the Internet by replacing its host-centric design with information-centric design. Communication among entities is established at the naming level, with the receiver side (referred to as the Consumer) acting as the driving force behind content delivery, by interacting with the network through Interest message transmissions. One of the proposed advantages for ICN is its support for mobility, by de-coupling applications from transport semantics. However, so far, little research has been conducted to understand the interaction between ICN and mobility of consuming and producing applications, in protocols purely based on information-centric principles, particularly in the case of NDN. In this paper, we present our findings on the mobility-based performance of Named Data Networking (NDN) in wireless access networks. Through simulations, we show that the current NDN architecture is not efficient in handling mobility and architectural enhancements needs to be done to fully support mobility of Consumers and Producers.Comment: to appear in IEEE ICC 201