Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

/pdf/the-structure-and-function-of-complex-networks-34deompc9l.pdf

The Structure and Function of Complex Networks

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out.

/pdf/power-law-distributions-in-empirical-data-4dybihkltl.pdf

Power-Law Distributions in Empirical Data

The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear dynamics, we would also like to understand how an enormous network of interacting dynamical systems-be they neurons, power stations or lasers-will behave collectively, given their individual dynamics and coupling architecture. Researchers are only now beginning to unravel the structure and dynamics of complex networks.

/pdf/exploring-complex-networks-2pdzihykyi.pdf

Exploring complex networks

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

We propose a random graph model which is a special case of sparse random graphs with given degree sequences. This model involves only a small number of parameters, called logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from these parameters, various properties of the graph can be derived. For example, for certain ranges of the parameters, we will compute the expected distribution of the sizes of the connected components which almost surely occur with high probability. We will illustrate the consistency of our model with the behavior of some massive graphs derived from data in telecommunications. We will also discuss the threshold function, the giant component, and the evolution of random graphs in this model.

/pdf/a-random-graph-model-for-massive-graphs-4f55ov5uui.pdf

A random graph model for massive graphs

We consider the question of protecting the privacy of customers buying digital goods. More specifically, our goal is to allow a buyer to purchase digital goods from a vendor without letting the vendor learn what, and to the extent possible also when and how much, it is buying. We propose solutions which allow the buyer, after making an initial deposit, to engage in an unlimited number of priced oblivious-transfer protocols, satisfying the following requirements: As long as the buyer's balance contains sufficient funds, it will successfully retrieve the selected item and its balance will be debited by the item's price. However, the buyer should be unable to retrieve an item whose cost exceeds its remaining balance. The vendor should learn nothing except what must inevitably be learned, namely, the amount of interaction and the initial deposit amount (which imply upper bounds on the quantity and total price of all information obtained by the buyer). In particular, the vendor should be unable to learn what the buyer's current balance is or when it actually runs out of its funds.

The technical tools we develop, in the process of solving this problem, seem to be of independent interest. In particular, we present the first one-round (two-pass) protocol for oblivious transfer that does not rely on the random oracle model (a very similar protocol was independently proposed by Naor and Pinkas [21]). This protocol is a special case of a more general "conditional disclosure" methodology, which extends a previous approach from [11] and adapts it to the 2-party setting.

/pdf/priced-oblivious-transfer-how-to-sell-digital-goods-21x923bufq.pdf

Priced Oblivious Transfer: How to Sell Digital Goods

We propose a random graph model which is a special case of sparserandom graphs with given degree sequences which satisfy a power law. This model involves only a small number of paramo eters, called logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. From these parameters, various properties of the graph can be derived. For example, for certai n ranges of the parameters, we wi II compute the expected distribution of the sizes of the connected components which almost surely occur with high probability. We illustrate the consistency of our model with the behavior of some massive graphs derived from data in telecommunications. We also discuss the threshold function, the giant component, and the evolution of random graphs in this model.

/pdf/a-random-graph-model-for-power-law-graphs-1t5ipgms9j.pdf

A random graph model for power law graphs

The smart grid introduces concerns for the loss of consumer privacy; recently deployed smart meters retain and distribute highly accurate profiles of home energy use. These profiles can be mined by Non Intrusive Load Monitors (NILMs) to expose much of the human activity within the served site. This paper introduces a new class of algorithms and systems, called Non Intrusive Load Leveling (NILL) to combat potential invasions of privacy. NILL uses an in-residence battery to mask variance in load on the grid, thus eliminating exposure of the appliance-driven information used to compromise consumer privacy. We use real residential energy use profiles to drive four simulated deployments of NILL. The simulations show that NILL exposes only 1.1 to 5.9 useful energy events per day hidden amongst hundreds or thousands of similar battery-suppressed events. Thus, the energy profiles exhibited by NILL are largely useless for current NILM algorithms. Surprisingly, such privacy gains can be achieved using battery systems whose storage capacity is far lower than the residence's aggregate load average. We conclude by discussing how the costs of NILL can be offset by energy savings under tiered energy schedules.

/pdf/protecting-consumer-privacy-from-electric-load-monitoring-2cjvjgd3oe.pdf

Protecting consumer privacy from electric load monitoring

BGP is essential to the operation of the Internet, but is vulnerable to both accidental failures and malicious attacks. We propose a new protocol that works in concert with BGP, which Autonomous Systems will use to help detect and mitigate accidentally or maliciously introduced faulty routing information. The protocol differs from previous efforts at securing BGP in that it is receiver-driven, meaning that there is a mechanism for recipients of BGP UPDATE messages to corroborate the information they receive and to provide feedback. We argue that our new protocol can be adopted incrementally, and we show that there is incentive for network operators to do so. We also describe our prototype implementation.

William Aiello

Papers

A random graph model for massive graphs

Priced Oblivious Transfer: How to Sell Digital Goods

A random graph model for power law graphs

Protecting consumer privacy from electric load monitoring

Working around BGP: An Incremental Approach to Improving Security and Accuracy in Interdomain Routing.