The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

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Statistical mechanics of complex networks

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.

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The Structure and Function of Complex Networks

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known—a collaboration network and a food web—and find that it detects significant and informative community divisions in both cases.

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Community structure in social and biological networks

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

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Finding and evaluating community structure in networks.

A system for indexing a document including: receiving a document to be processed for inclusion in an index of documents; locating a set of documents that include hyperlinks to the document; retrieving anchortext associated with each hyperlink; parsing the anchortext into one or more tokens. Then for each token the following acts are performed: determining a weight for the token, determining whether the weight assigned to the token exceeds a threshold token weight; and indexing the document under the token, if the token weight assigned to the token exceeds the threshold token weight.

Method for ranking web page search results

Traditional document classification frameworks, which apply the learned classifier to each document in a corpus one by one, are infeasible for extremely large document corpora, like the Web or large corporate intranets. We consider the classification problem on a corpus that has been processed primarily for the purpose of searching, and thus our access to documents is solely through the inverted index of a large scale search engine. Our main goal is to build the "best" short query that characterizes a document class using operators normally available within large engines. We show that surprisingly good classification accuracy can be achieved on average over multiple classes by queries with as few as 10 terms. Moreover, we show that optimizing the efficiency of query execution by careful selection of these terms can further reduce the query costs. More precisely, we show that on our set-up the best 10 terms query canachieve 90% of the accuracy of the best SVM classifier (14000 terms), and if we are willing to tolerate a reduction to 86% of the best SVM, we can build a 10 terms query that can be executed more than twice as fast as the best 10 terms query.

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Effective and efficient classification on a search-engine model

Ranking Web search results has long evolved beyond simple bag-of-words retrieval models. Modern search engines routinely employ machine learning ranking that relies on exogenous relevance signals. Yet the majority of current methods still evaluate each Web page out of context. In this work, we introduce a novel source of relevance information for Web search by evaluating each page in the context of its host Web site. For this purpose, we devise two strategies for compactly representing entire Web sites. We formalize our approach by building two indices, a traditional page index and a new site index, where each "document" represents the an entire Web site. At runtime, a query is first executed against both indices, and then the final page score for a given query is produced by combining the scores of the page and its site. Experimental results carried out on a large-scale Web search test collection from a major commercial search engine confirm the proposed approach leads to consistent and significant improvements in retrieval effectiveness.

Exploiting site-level information to improve web search

Methods for selecting advertisements to serve to a client requesting a primary webpage is provided The client displays a referring webpage having a hyperlink to the primary webpage Upon selection of the hyperlink, the client sends a request to a content server storing the primary webpage, the request including a referrer of the primary webpage comprising a URL address of the referring webpage The content server sends the primary webpage to the client which includes the referrer and an advertisement request mechanism configured to make an advertisement request to an advertisement server and attach the referrer to the advertisement request The advertisement server uses the referrer to select one or more advertisements to serve to the client The referrer may comprise one or more search query terms submitted by the client The advertisement server may also use the content of the primary webpage to select the one or more advertisements

Serving Advertisements with a Webpage Based on a Referrer Address of the Webpage

The classic Web search experience, consisting of returning "ten blue links" in response to a short user query, is powered today by a mature technology where progress has become incremental and expensive. Furthermore, the "ten blue links" represent only a fractional part of the total Web search experience: today, what users expect and receive in response to a "web query" is a plethora of multi-media information extracted and synthesized from numerous sources on and off the Web. In consequence, we argue that the major technical challenges in Web search are now driven by the quest to satisfy the implicit and explicit needs of users, continuing a long evolutionary trend in commercial Web search engines going back more than fifteen years, moving from relevant document selection towards satisfactory task completion. We identify seven of these challenges and discuss them in some detail.

Andrei Z. Broder

Papers

Method for ranking web page search results

Effective and efficient classification on a search-engine model

Exploiting site-level information to improve web search

Serving Advertisements with a Webpage Based on a Referrer Address of the Webpage

The new frontier of web search technology: seven challenges