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Biomedical subjects

M E J Newman

Publications and source records attributed to M E J Newman.

At least 19 recordsLinked to original sources
PubMed2006

Exact solutions for models of evolving networks with addition and deletion of nodes.

There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied. In the real world, however, many networks, including the web, not only add vertices but also lose them. Here we formulate models of the time evolution of such networks and give exact solutions for a number of cases of particular interest. For the case of net growth and so-called preferential attachment--in which newly appearing vertices attach to previously existing ones in proportion to vertex degree--we show that the resulting networks have power-law degree distributions, but with an exponent that diverges as the growth rate vanishes. We conjecture that the low exponent values observed in real-world networks are thus the result of vigorous growth in which the rate of addition of vertices far exceeds the rate of removal. Were growth to slow in the future--for instance, in a more mature future version of the web--we would expect to see exponents increase, potentially without bound.

Journal Article↗
PubMed2006

Finding community structure in networks using the eigenvectors of matrices.

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.

Journal Article↗
PubMed2006

Optimal design of spatial distribution networks.

We consider the problem of constructing facilities such as hospitals, airports, or malls in a country with a nonuniform population density, such that the average distance from a person's home to the nearest facility is minimized. We review some previous approximate treatments of this problem that indicate that the optimal distribution of facilities should have a density that increases with population density, but does so slower than linearly, as the two-thirds power. We confirm this result numerically for the particular case of the United States with recent population data using two independent methods, one a straightforward regression analysis, the other based on density-dependent map projections. We also consider strategies for linking the facilities to form a spatial network, such as a network of flights between airports, so that the combined cost of maintenance of and travel on the network is minimized. We show specific examples of such optimal networks for the case of the United States.

Journal Article↗
PubMed2006

Modularity and community structure in networks.

Many networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure is one of the outstanding issues in the study of networked systems. One highly effective approach is the optimization of the quality function known as "modularity" over the possible divisions of a network. Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times. I illustrate the method with applications to several published network data sets.

Journal Article↗
PubMed2006

Vertex similarity in networks.

We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads to a self-consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network. We test our similarity measure on computer-generated networks for which the expected results are known, and on a number of real-world networks.

Animals↗
PubMed2005

Predicting epidemics on directed contact networks.

Contact network epidemiology is an approach to modeling the spread of infectious diseases that explicitly considers patterns of person-to-person contacts within a community. Contacts can be asymmetric, with a person more likely to infect one of their contacts than to become infected by that contact. This is true for some sexually transmitted diseases that are more easily caught by women than men during heterosexual encounters; and for severe infectious diseases that cause an average person to seek medical attention and thereby potentially infect health care workers (HCWs) who would not, in turn, have an opportunity to infect that average person. Here we use methods from percolation theory to develop a mathematical framework for predicting disease transmission through semi-directed contact networks in which some contacts are undirected-the probability of transmission is symmetric between individuals-and others are directed-transmission is possible only in one direction. We find that the probability of an epidemic and the expected fraction of a population infected during an epidemic can be different in semi-directed networks, in contrast to the routine assumption that these two quantities are equal. We furthermore demonstrate that these methods more accurately predict the vulnerability of HCWs and the efficacy of various hospital-based containment strategies during outbreaks of severe respiratory diseases.

Communicable Disease Control↗
PubMed2005

Threshold effects for two pathogens spreading on a network.

Diseases spread through host populations over the networks of contacts between individuals and a number of results about this process have been derived in recent years by exploiting connections between epidemic processes and bond percolation on networks. Here we investigate the case of two pathogens in a single population, which has been the subject of recent interest among epidemiologists. We demonstrate that two pathogens competing for the same hosts can both spread through a population only for intermediate values of the bond occupation probability that lie above the classic epidemic threshold and below a second higher value, which we call the coexistence threshold, corresponding to a distinct topological phase transition in networked systems.

Communicable Diseases↗
PubMed2005

Solution for the properties of a clustered network.

We study Strauss's model of a network with clustering and present an analytic mean-field solution which is exact in the limit of large network size. Previous computer simulations have revealed a degenerate region in the model's parameter space in which triangles of adjacent edges clump together to form unrealistically dense subgraphs, and perturbation calculations have been found to break down in this region at all orders. Our solution shows that this region corresponds to a classic symmetry-broken phase and that the onset of the degeneracy corresponds to a first-order phase transition in the density of the network.

Journal Article↗
PubMed2005

A network analysis of committees in the U.S. House of Representatives.

Network theory provides a powerful tool for the representation and analysis of complex systems of interacting agents. Here, we investigate the U.S. House of Representatives network of committees and subcommittees, with committees connected according to "interlocks," or common membership. Analysis of this network reveals clearly the strong links between different committees, as well as the intrinsic hierarchical structure within the House as a whole. We show that network theory, combined with the analysis of roll-call votes using singular value decomposition, successfully uncovers political and organizational correlations between committees in the House without the need to incorporate other political information.

Journal Article↗
PubMed2005

Network theory and SARS: predicting outbreak diversity.

Many infectious diseases spread through populations via the networks formed by physical contacts among individuals. The patterns of these contacts tend to be highly heterogeneous. Traditional "compartmental" modeling in epidemiology, however, assumes that population groups are fully mixed, that is, every individual has an equal chance of spreading the disease to every other. Applications of compartmental models to Severe Acute Respiratory Syndrome (SARS) resulted in estimates of the fundamental quantity called the basic reproductive number R0--the number of new cases of SARS resulting from a single initial case--above one, implying that, without public health intervention, most outbreaks should spark large-scale epidemics. Here we compare these predictions to the early epidemiology of SARS. We apply the methods of contact network epidemiology to illustrate that for a single value of R0, any two outbreaks, even in the same setting, may have very different epidemiological outcomes. We offer quantitative insight into the heterogeneity of SARS outbreaks worldwide, and illustrate the utility of this approach for assessing public health strategies.

Adult↗
PubMed2004

Solution of the two-star model of a network.

The p-star model or exponential random graph is among the oldest and best known of network models. Here we give an analytic solution for the particular case of the two-star model, which is one of the most fundamental of exponential random graphs. We derive expressions for a number of quantities of interest in the model and show that the degenerate region of the parameter space observed in computer simulations is a spontaneously symmetry-broken phase separated from the normal phase of the model by a conventional continuous phase transition.

Journal Article↗
PubMed2004

Identifying the role that animals play in their social networks.

Techniques recently developed for the analysis of human social networks are applied to the social network of bottlenose dolphins living in Doubtful Sound, New Zealand. We identify communities and subcommunities within the dolphin population and present evidence that sex- and age-related homophily play a role in the formation of clusters of preferred companionship. We also identify brokers who act as links between sub-communities and who appear to be crucial to the social cohesion of the population as a whole. The network is found to be similar to human social networks in some respects but different in some others, such as the level of assortative mixing by degree within the population. This difference elucidates some of the means by which the network forms and evolves.

Age Factors↗
PubMed2004

Statistical mechanics of networks.

We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the same role in the study of networks as is played by the Boltzmann distribution in classical statistical mechanics; they offer the best prediction of network properties subject to the constraints imposed by a given set of observations. We give exact solutions of models within this class that incorporate arbitrary degree distributions and arbitrary but independent edge probabilities. We also discuss some more complex examples with correlated edges that can be solved approximately or exactly by adapting various familiar methods, including mean-field theory, perturbation theory, and saddle-point expansions.

Journal Article↗
PubMed2004

Finding community structure in very large networks.

The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O (md log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m approximately n and d approximately log n, in which case our algorithm runs in essentially linear time, O (n log(2) n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on-line retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400 000 vertices and 2 x 10(6) edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.

Journal Article↗
PubMed2004

Analysis of weighted networks.

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum-flow-minimum-cut theorem.

Journal Article↗
PubMed2004

Fast algorithm for detecting community structure in networks.

Many networks display community structure--groups of vertices within which connections are dense but between which they are sparser--and sensitive computer algorithms have in recent years been developed for detecting this structure. These algorithms, however, are computationally demanding, which limits their application to small networks. Here we describe an algorithm which gives excellent results when tested on both computer-generated and real-world networks and is much faster, typically thousands of times faster, than previous algorithms. We give several example applications, including one to a collaboration network of more than 50,000 physicists.

Journal Article↗
PubMed2004

From The Cover: Diffusion-based method for producing density-equalizing maps.

Map makers have for many years searched for a way to construct cartograms, maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some other analogous property. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of human data. Unfortunately, to scale regions and still have them fit together, one is normally forced to distort the regions' shapes, potentially resulting in maps that are difficult to read. Many methods for making cartograms have been proposed, some of them are extremely complex, but all suffer either from this lack of readability or from other pathologies, like overlapping regions or strong dependence on the choice of coordinate axes. Here, we present a technique based on ideas borrowed from elementary physics that suffers none of these drawbacks. Our method is conceptually simple and produces useful, elegant, and easily readable maps. We illustrate the method with applications to the results of the 2000 U.S. presidential election, lung cancer cases in the State of New York, and the geographical distribution of stories appearing in the news.

Data Interpretation, Statistical↗