arXiv subjects

M. E. J. Newman

Publications and source records attributed to M. E. J. Newman.

At least 127 records · Page 7Linked to original sources

arXiv2002

Assortative mixing in networks

A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. We define a measure of assortative mixing for networks and use it to show that social networks are often assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortative network, which we study both analytically and numerically. Within the framework of this model we find that assortative networks tend to percolate more easily than their disassortative counterparts and that they are also more robust to vertex removal.

cond-mat.dis-nn↗

arXiv2002

Identity and Search in Social Networks

Social networks have the surprising property of being "searchable": Ordinary people are capable of directing messages through their network of acquaintances to reach a specific but distant target person in only a few steps. We present a model that offers an explanation of social network searchability in terms of recognizable personal identities: sets of characteristics measured along a number of social dimensions. Our model defines a class of searchable networks and a method for searching them that may be applicable to many network search problems, including the location of data files in peer-to-peer networks, pages on the World Wide Web, and information in distributed databases.

cond-mat.dis-nn↗

arXiv2002

The spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.

cond-mat.stat-mech↗

arXiv2002

Convergence of threshold estimates for two-dimensional percolation

Using a recently introduced algorithm for simulating percolation in microcanonical (fixed-occupancy) samples, we study the convergence with increasing system size of a number of estimates for the percolation threshold for an open system with a square boundary, specifically for site percolation on a square lattice. We show that the convergence of the so-called "average-probability" estimate is described by a non-trivial correction-to-scaling exponent as predicted previously, and measure the value of this exponent to be 0.90(2). For the "median" and "cell-to-cell" estimates of the percolation threshold we verify that convergence does not depend on this exponent, having instead a slightly faster convergence with a trivial analytic leading exponent.

cond-mat.stat-mech↗

arXiv2002

Optimal design, robustness, and risk aversion

Highly optimized tolerance is a model of optimization in engineered systems, which gives rise to power-law distributions of failure events in such systems. The archetypal example is the highly optimized forest fire model. Here we give an analytic solution for this model which explains the origin of the power laws. We also generalize the model to incorporate risk aversion, which results in truncation of the tails of the power law so that the probability of disastrously large events is dramatically lowered, giving the system more robustness.

cond-mat.stat-mech↗

arXiv2002

Random graphs as models of networks

The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks such as the Internet, social networks or biological networks it leaves a lot to be desired. In particular, it differs from real networks in two crucial ways: it lacks network clustering or transitivity, and it has an unrealistic Poissonian degree distribution. In this paper we review some recent work on generalizations of the random graph aimed at correcting these shortcomings. We describe generalized random graph models of both directed and undirected networks that incorporate arbitrary non-Poisson degree distributions, and extensions of these models that incorporate clustering too. We also describe two recent applications of random graph models to the problems of network robustness and of epidemics spreading on contact networks.

cond-mat.stat-mech↗

arXiv2002

Exact solutions of epidemic models on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed models, and many of their generalizations, can be solved exactly on a wide variety of networks. Solutions are possible for cases with heterogeneous or correlated probabilities of transmission, cases incorporating vaccination, and cases in which the network has complex structure of various kinds. We confirm the correctness of our solutions by comparison with computer simulations of epidemics propagating on the corresponding networks.

cond-mat.stat-mech↗

arXiv2001

Community structure in social and biological networks

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the World-Wide Web. Researchers have concentrated particularly on a few properties which seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this paper, we highlight another property which 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 new 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 it 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.

cond-mat.stat-mech↗

arXiv2001

Ego-centered networks and the ripple effect

Recent work has demonstrated that many social networks, and indeed many networks of other types also, have broad distributions of vertex degree. Here we show that this has a substantial impact on the shape of ego-centered networks, i.e., sets of network vertices that are within a given distance of a specified central vertex, the ego. This in turn affects concepts and methods based on ego-centered networks, such as snowball sampling and the "ripple effect". In particular, we argue that one's acquaintances, one's immediate neighbors in the acquaintance network, are far from being a random sample of the population, and that this biases the numbers of neighbors two and more steps away. We demonstrate this concept using data drawn from academic collaboration networks, for which, as we show, current simple theories for the typical size of ego-centered networks give numbers that differ greatly from those measured in reality. We present an improved theoretical model which gives significantly better results.

cond-mat.stat-mech↗

arXiv2001

Percolation and epidemics in a two-dimensional small world

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of "shortcuts" in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.

cond-mat.stat-mech↗

arXiv2001

Dynamics of a simple evolutionary process

We study the simple evolutionary process in which we repeatedly find the least fit agent in a population of agents and give it a new fitness which is chosen independently at random from a specified distribution. We show that many of the average properties of this process can be calculated exactly using analytic methods. In particular we find the distribution of fitnesses at arbitrary time, and the distribution of the lengths of runs of hits on the same agent, the latter being found to follow a power law with exponent -1, similar to the distribution of times between evolutionary events in the Bak-Sneppen model and models based on the so-called record dynamics. We confirm our analytic results with extensive numerical simulations.

nlin.AO↗

arXiv2001

Are randomly grown graphs really random?

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time steps. In the limit of large t, the resulting graph displays surprisingly rich characteristics. In particular, a giant component emerges in an infinite-order phase transition at delta = 1/8. At the transition, the average component size jumps discontinuously but remains finite. In contrast, a static random graph with the same degree distribution exhibits a second-order phase transition at delta = 1/4, and the average component size diverges there. These dramatic differences between grown and static random graphs stem from a positive correlation between the degrees of connected vertices in the grown graph--older vertices tend to have higher degree, and to link with other high-degree vertices, merely by virtue of their age. We conclude that grown graphs, however randomly they are constructed, are fundamentally different from their static random graph counterparts.

cond-mat.stat-mech↗

arXiv2001

A Simple Model of Epidemics with Pathogen Mutation

We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted individuals becoming infected only if they are exposed to strains that are significantly different from other strains in their memory repertoire. The second model is a reduction of the first to a system of difference equations. In this case, individuals spend a fixed amount of time in a generalized immune class. In both models, we observe four fundamentally different types of behavior, depending on parameters: (1) pathogen extinction due to lack of contact between individuals, (2) endemic infection (3) periodic epidemic outbreaks, and (4) one or more outbreaks followed by extinction of the epidemic due to extremely low minima in the oscillations. We analyze both models to determine the location of each transition. Our main result is that pathogens in highly connected populations must mutate rapidly in order to remain viable.

nlin.CD↗

arXiv2001

Random graphs with arbitrary degree distributions and their applications

Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in the past. In this paper we develop in detail the theory of random graphs with arbitrary degree distributions. In addition to simple undirected, unipartite graphs, we examine the properties of directed and bipartite graphs. Among other results, we derive exact expressions for the position of the phase transition at which a giant component first forms, the mean component size, the size of the giant component if there is one, the mean number of vertices a certain distance away from a randomly chosen vertex, and the average vertex-vertex distance within a graph. We apply our theory to some real-world graphs, including the world-wide web and collaboration graphs of scientists and Fortune 1000 company directors. We demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.

cond-mat.stat-mech↗

arXiv2001

Clustering and preferential attachment in growing networks

We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators. These results provide experimental evidence in favor of previously conjectured mechanisms for clustering and power-law degree distributions in networks.

cond-mat.stat-mech↗

arXiv2001

A fast Monte Carlo algorithm for site or bond percolation

We describe in detail a new and highly efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time which scales linearly with the size of the system. We demonstrate our algorithm by using it to investigate a number of issues in percolation theory, including the position of the percolation transition for site percolation on the square lattice, the stretched exponential behavior of spanning probabilities away from the critical point, and the size of the giant component for site percolation on random graphs.

cond-mat.stat-mech↗

arXiv2000

Who is the best connected scientist? A study of scientific coauthorship networks

Using data from computer databases of scientific papers in physics, biomedical research, and computer science, we have constructed networks of collaboration between scientists in each of these disciplines. In these networks two scientists are considered connected if they have coauthored one or more papers together. We have studied many statistical properties of our networks, including numbers of papers written by authors, numbers of authors per paper, numbers of collaborators that scientists have, typical distance through the network from one scientist to another, and a variety of measures of connectedness within a network, such as closeness and betweenness. We further argue that simple networks such as these cannot capture the variation in the strength of collaborative ties and propose a measure of this strength based on the number of papers coauthored by pairs of scientists, and the number of other scientists with whom they coauthored those papers. Using a selection of our results, we suggest a variety of possible ways to answer the question "Who is the best connected scientist?"

cond-mat.stat-mech↗

arXiv2000

Efficient Monte Carlo algorithm and high-precision results for percolation

We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice. We use our algorithm to determine that the percolation transition occurs at occupation probability 0.59274621(13) for site percolation on the square lattice and to provide clear numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.

cond-mat.stat-mech↗