Papers in refereed journals:

Notes:
  • Each paper's `# Times Cited' is as was reported by ISI Web of Knowledge, October 18, 2009.
  • 802 total citations for 21 papers in print.
  • h-index = 12.
  • Formal fields include: Physics, Applied Mathematics, Geomorphology, Geophysics, Biology, Economics, Sociology, Psychology, and Marketing.
  • Journals include: Science Magazine, Proceedings of the National Academy of Sciences, Physical Review Letters, Physical Review E, Journal of Theoretical Biology, Annual Review of Earth & Planetary Sciences, Journal of Happiness Studies, Journal of Consumer Research, Management Science, Marketing Letters.
  • Papers are listed in reverse chronological order.

expand all abstracts | contract all abstracts

[21] J. L. Payne, P. S. Dodds, and M. J. Eppstein.
"Information cascades on degree-correlated random networks."
Physical Review E, 80, 026125, 2009.
# Times Cited: -
[download reprint]
Abstract
We investigate by numerical simulation a threshold model of social contagion on degree-correlated random networks. We show that the class of networks for which global info rmation cascades occur generally expands as degree-degree correlations become increasingly positive. However, under certain conditions, large-scale information cascades ca n paradoxically occur when degree-degree correlations are sufficiently positive or negative, but not when correlations are relatively small. We also show that the relation ship between the degree of the initially infected vertex and its ability to trigger large cascades is strongly affected by degree-degree correlations.

[20] P. S. Dodds and C. M. Danforth.
"Measuring the Happiness of Large-Scale Written Expression: Songs, Blogs, and Presidents."
Journal of Happiness Studies, DOI: 10.1007/s10902-009-9150-9, Published online July 20, 2009.
# Times Cited: -
[download reprint]
Abstract
The importance of quantifying the nature and intensity of emotional states at the level of populations is evident: we would like to know how, when, and why individuals feel as they do if we wish, for example, to better construct public policy, build more successful organizations, and, from a scientific perspective, more fully understand economic and social phenomena. Here, by incorporating direct human assessment of words, we quantify happiness levels on a continuous scale for a diverse set of large-scale texts: song titles and lyrics, weblogs, and State of the Union addresses. Our method is transparent, improvable, capable of rapidly processing Web-scale texts, and moves beyond approaches based on coarse categorization. Among a number of observations, we find that the happiness of song lyrics trends downward from the 1960's to the mid 1990's while remaining stable within genres, and that the happiness of blogs has steadily increased from 2005 to 2009, exhibiting a striking rise and fall with blogger age and distance from the equator.

[19] P. S. Dodds and J. L. Payne.
"Analysis of a threshold model of social contagion on degree-correlated networks."
Physical Review E, 79, 066115, 2009.
# Times Cited: 1
[download reprint]
Abstract
We analytically determine when a range of abstract social contagion models permit global spreading from a single seed on degree-correlated, undirected random networks. We deduce the expected size of the largest vulnerable component, a network's tinderbox-like critical mass, as well as the probability that infecting a randomly chosen individual seed will trigger global spreading. In the appropriate limits, our results naturally reduce to standard ones for models of disease spreading and to the condition for the existence of a giant component. Recent advances in the distributed, infinite seed case allow us to further determine the final size of global spreading events, when they occur. To provide support for our results, we derive exact expressions for key spreading quantities for a simple yet rich family of random networks with bimodal degree distributions.

[18] W. R. Hartmann, P. Manchanda, H. Nair, M. Bothner, P. S. Dodds, D. Godes, K. Hosanager, and C. Tucker.
"Modeling social interactions: Identification, empirical methods and policy implications."
Marketing Letters, 19, 287-304, 2008.
# Times Cited: 1
[download reprint]
Abstract
Social interactions occur when agents in a network affect other agents’ choices directly, as opposed to via the intermediation of markets. The study of such interactions and the resultant outcomes has long been an area of interest across a wide variety of social sciences. With the advent of electronic media that facilitate and record such interactions, this interest has grown sharply in the business world as well. In this paper, we provide a brief summary of what is known so far, discuss the main challenges for researchers interested in this area and provide a common vocabulary that will hopefully engender future (cross-disciplinary) research. The paper considers the challenges of distinguishing actual causal social interactions from other phenomena that may lead to a false inference of causality. Further, we distinguish between two broadly defined types of social interactions that relate to how strongly interactions spread through a network. We also provide a very selective review of how insights from other disciplines can improve and inform modeling choices. Finally, we discuss how models of social interaction can be used to provide guidelines for marketing policy and conclude with thoughts on future research directions.

[17] D. J. Watts and P. S. Dodds.
"Influentials, Networks, and Public Opinion Formation."
Journal of Consumer Research, 34, 441-458, 2007.
# Times Cited: 9
[download reprint]
Abstract
A central idea in marketing and diffusion research is that influentials—a minority of individuals who influence an exceptional number of their peers—are important to the formation of public opinion. Here we examine this idea, which we call the “influentials hypothesis,” using a series of computer simulations of interpersonal influence processes. Under most conditions that we consider, we find that large cascades of influence are driven not by influentials but by a critical mass of easily influenced individuals. Although our results do not exclude the possibility that influentials can be important, they suggest that the influentials hypothesis requires more careful specification and testing than it has received.

[16] N. Hanaki, A. Peterhansl, P. S. Dodds, and D. J. Watts.
``Cooperation in evolving social networks.''
Management Science, 53, 1036-1050, 2007.
# Times Cited: 13
[download reprint]
Abstract
We study the problem of cooperative behavior emerging in an environment where individual behaviors and interaction structures coevolve. Players not only learn which strategy to adopt by imitating the strategy of the best-performing player they observe, but also choose with whom they should interact by selectively creating and/or severing ties with other players based on a myopic cost-benefit comparison. We find that scalable cooperation—that is, high levels of cooperation in large populations—can be achieved in sparse networks, assuming that individuals are able to sever ties unilaterally and that new ties can only be created with the mutual consent of both parties. Detailed examination shows that there is an important trade-off between local reinforcement and global expansion in achieving cooperation in dynamic networks. As a result, networks in which ties are costly and local structure is largely absent tend to generate higher levels of cooperation than those in which ties are made easily and friends of friends interact with high probability, where the latter result contrasts strongly with the usual intuition.

[15] M. J. Salganik, P. S. Dodds, and D. J. Watts.
``Experimental study of inequality and unpredictability in an artificial cultural market.''
Science, 311, 854-856, 2006.
# Times Cited: 54
[download reprint] [download supplementary material]
Abstract
Hit songs, books, and movies are many times more successful than average, suggesting that ``the best'' alternatives are qualitatively different from ``the rest''; yet experts routinely fail to predict which products will succeed. We investigated this paradox experimentally, by creating an artificial ``music market'' in which 14,341 participants downloaded previously unknown songs either with or without knowledge of previous participants' choices. Increasing the strength of social influence increased both inequality and unpredictability of success. Success was also only partly determined by quality: The best songs rarely did poorly, and the worst rarely did well, but any other result was possible.

[14] D. J. Watts, R. Muhamad, D. C. Medina, and P. S. Dodds.
``Multiscale, resurgent epidemics in a hierarchical metapopulation model.''
Proc. Natl. Acad. Sci., 102, 11157-11162, 2005.
# Times Cited: 38
[download reprint]
Abstract
Although population structure has long been recognized as relevant to the spread of infectious disease, traditional mathematical models have understated the role of nonhomogenous mixing in populations with geographical and social structure. Recently, a wide variety of spatial and network models have been proposed that incorporate various aspects of interaction structure among individuals. However, these more complex models necessarily suffer from limited tractability, rendering general conclusions difficult to draw. In seeking a compromise between parsimony and realism, we introduce a class of metapopulation models in which we assume homogeneous mixing holds within local contexts, and that these contexts are embedded in a nested hierarchy of successively larger domains. We model the movement of individuals between contexts via simple transport parameters and allow diseases to spread stochastically. Our model exhibits some important stylized features of real epidemics, including extreme size variation and temporal heterogeneity, that are difficult to characterize with traditional measures. In particular, our results suggest that when epidemics do occur the basic reproduction number R0 may bear little relation to their final size. Informed by our model's behavior, we suggest measures for characterizing epidemic thresholds and discuss implications for the control of epidemics.

[13] P. S. Dodds and D. J. Watts.
``A generalized model of social and biological contagion.''
Journal of Theoretical Biology, 232, 587-604, 2005.
# Times Cited: 12
[download reprint]
Abstract
We present a model of contagion that unifies and generalizes threshold models of social contagion and epidemiological models of disease spreading. Our model incorporates individual memory of exposure to a contagious entity (e.g., a rumor or disease), variable magnitudes of exposure (dose sizes), and heterogeneity in the susceptibility of individuals. Through analysis and simulation, we examine in detail the case where individuals may recover from an infection and then immediately become susceptible again (analogous to the so-called SIS model). We identify three basic classes of contagion models which we call epidemic threshold, vanishing critical mass, and critical mass classes respectively, where each class of models corresponds to different strategies for prevention or facilitation. We find that the conditions for a particular contagion model to belong to one of the these three classes depend only on memory length and the probabilities of being infected by one and two exposures respectively. These parameters are in principle measurable for real contagious influences or entities, thus yielding empirical implications for our model. We also study the case where individuals attain permanent immunity once recovered, finding that epidemics inevitably die out but may be surprisingly persistent when individuals possess memory.

[12] P. S. Dodds and D. J. Watts.
``Universal Behavior in a Generalized Model of Contagion.''
Phyical Review Letters, 92, article #218701, 2004.
# Times Cited: 24
[download reprint]
Abstract
Models of contagion arise broadly both in the biological and social sciences, with applications ranging from the transmission of infectious diseases to the diffusion of innovations and the spread of cultural fads. In this Letter, we introduce a general model of contagion which, by explicitly incorporating memory of past exposures to, for example, an infectious agent, rumor, or new product, includes the main features of existing contagion models and interpolates between them. We obtain exact solutions for a simple version of the model, finding that under general conditions only three classes of collective dynamics exist, two of which correspond to familiar epidemic threshold and critical mass dynamics, while the third is a distinct intermediate case. We find that for a given length of memory, the class into which a particular system falls is determined by two parameters, each of which ought to be measurable empirically. Our model suggests novel measures for assessing the susceptibility of a population to large contagion events, and also a possible strategy for inhibiting or facilitating them.

[11] P. S. Dodds, D. J. Watts, and C. F. Sabel.
``Information exchange and the robustness of organizational networks.''
Proc. Natl. Acad. Sci., 100, 12516-12521, 2003.
# Times Cited: 28
[download reprint]
Abstract
The dynamics of information exchange is an important but understudied aspect of collective communication, coordination, and problem solving in a wide range of distributed systems, both physical (e.g., the Internet) and social (e.g., business firms). In this paper, we introduce a model of organizational networks according to which links are added incrementally to a hierarchical backbone and test the resulting networks under variable conditions of information exchange. Our main result is the identification of a class of multiscale networks that reduce, over a wide range of environments, the likelihood that individual nodes will suffer congestion-related failure and that the network as a whole will disintegrate when failures do occur. We call this dual robustness property of multiscale networks "ultrarobustness." Furthermore, we find that multiscale networks attain most of their robustness with surprisingly few link additions, suggesting that ultrarobust organizational networks can be generated in an efficient and scalable manner. Our results are directly relevant to the relief of congestion in communication networks and also more broadly to activities, like distributed problem solving, that require individuals to exchange information in an unpredictable manner.

[10] P. S. Dodds, R. Muhamad, and D. J. Watts.
``An Experimental study of search in global social networks.''
Science, 301, 827-829, 2003.
# Times Cited: 90
[download reprint] [download supplementary material]
Abstract
We report on a global social-search experiment in which more than 60,000 e-mail users attempted to reach one of 18 target persons in 13 countries by forwarding messages to acquaintances. We find that successful social search is conducted primarily through intermediate to weak strength ties, does not require highly connected "hubs" to succeed, and, in contrast to unsuccessful social search, disproportionately relies on professional relationships. By accounting for the attrition of message chains, we estimate that social searches can reach their targets in a median of five to seven steps, depending on the separation of source and target, although small variations in chain lengths and participation rates generate large differences in target reachability. We conclude that although global social networks are, in principle, searchable, actual success depends sensitively on individual incentives.

[9] P. S. Dodds and J. S. Weitz.
``Packing-limited growth of irregular objects.''
Physical Review E, 67, 016117, 2003.
# Times Cited: 4
[download reprint]
Abstract
We study growth limited by packing for irregular objects in two dimensions. We generate packings by seeding objects randomly in time and space and allowing each object to grow until it collides with another object. The objects we consider, allow us to investigate the separate effects of anisotropy and non-unit aspect ratio. By means of a connection to the decay of pore-space volume, we measure power law exponents for the object size distribution. We carry out a mean field analysis, showing that it provides an upper bound for the size distribution exponent. We find that while the details of the growth mechanism are irrelevent, the exponent is strongly shape dependent. Potential applications lie in ecological and biological environments where sessile organisms compete for limited space as they grow.

[8] D. J. Watts, P. S. Dodds and M. E. J. Newman.
``Identity and search in social networks''
Science, 296, 1302-1305, 2002.
# Times Cited: 203
[download reprint]
Abstract
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.

[7] P.S. Dodds and J.S. Weitz.
``Packing-limited growth.''
Physical Review E, 65, 056108, 2002.
# Times Cited: 12
[download reprint]
Abstract
We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via simulation in d=2, 3, and 4. We show how a broad class of such models exhibit distributions of sphere radii with a universal exponent. We construct a scaling theory which relates the fractal structure of these models to the decay of their pore space, a theory which we confirm via numerical simulations. The scaling theory also predicts an upper bound for the universal exponent and is in exact agreement with numerical results for d=4.

[6] P. S. Dodds, D. H. Rothman, and J. S. Weitz.
``Re-examination of the `3/4-law' of Metabolism,''
Journal of Theoretical Biology, 209, 9-27, 2001.
# Times Cited: 178
[download reprint]
Abstract
We examine the scaling law B=cMα which connects organismal resting metabolic rate B with organismal mass M, where α is commonly held to be 3/4. Since simple dimensional analysis suggests α=2/3, we consider this to be a null hypothesis testable by empirical studies. We re-analyze data sets for mammals and birds compiled by Heusner, Bennett and Harvey, Bartels, Hemmingsen, Brody, and Kleiber, and find little evidence for rejecting α=2/3 in favor of α=3/4. For mammals, we find a possible breakdown in scaling for larger masses reflected in a systematic increase in α. We also review theoretical justifications of α=3/4 based on dimensional analysis, nutrient-supply networks, and four-dimensional biology. We find that present theories for α=3/4 require assumptions that render them unconvincing for rejecting the null hypothesis that α=2/3.

[5] P. S. Dodds and D. H. Rothman.
``Geometry of River Networks III: Characterization of Component Connectivity,''
Physical Review E, 63, 016117, 2001.
# Times Cited: 6
[download reprint]
Abstract
Essential to understanding the overall structure of river networks is a knowledge of their detailed architecture. Here, we explore the presence of randomness in river network structure and the details of its consequences. We first show that an averaged view of network architecture is provided by a proposed self-similarity statement about the scaling of drainage density, a local measure of stream concentration. This scaling of drainage density is shown to imply Tokunaga's law, a description of the scaling of side branch abundance along a given stream, as well as a scaling law for stream lengths. We then consider fluctuations in drainage density and consequently the numbers of side branches. Data is analyzed for the Mississippi River basin and a model of random directed networks. Numbers of side streams are found to follow exponential distributions as are inter-tributary distances along streams. Finally, we derive the joint variation of side stream abundance with stream length, affording a full description of fluctuations in network structure. Fluctuations in side stream numbers are shown to be a direct result of fluctuations in stream lengths. This is the last paper in a series of three on the geometry of river networks.

[4] P.S. Dodds and D.H. Rothman.
``Geometry of River Networks II: Distributions of Component Size and Number,''
Physical Review E, 63, 016116, 2001.
# Times Cited: 5
[download reprint]
Abstract
The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length-scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.

[3] P. S. Dodds and D. H. Rothman.
``Geometry of River Networks I: Scaling, Fluctuations, and Deviations,''
Physical Review E, 63, 016115, 2001.
# Times Cited: 16
[download reprint]
Abstract
This article is the first in a series of three papers investigating the detailed geometry of river networks. Branching networks are a universal structure employed in the distribution and collection of material. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description of river network structure, scaling laws are uniformly observed. Reported values of scaling exponents vary suggesting that no unique set of scaling exponents exists. To improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure, here we report a theoretical and empirical study of fluctuations about and deviations from scaling. We examine data for continent-scale river networks such as the Mississippi and the Amazon and draw inspiration from a simple model of directed, random networks. We center our investigations on the scaling of the length of a sub-basin's dominant stream with its area, a characterization of basin shape known as Hack's law. We generalize this relationship to a joint probability density and provide observations and explanations of deviations from scaling. We show that fluctuations about scaling are substantial and grow with system size. We find strong deviations from scaling at small scales which can be explained by the existence of linear network structure. At intermediate scales, we find slow drifts in exponent values indicating that scaling is only approximately obeyed and that universality remains indeterminate. At large scales, we observe a breakdown in scaling due to decreasing sample space and correlations with overall basin shape. The extent of approximate scaling is significantly restricted by these deviations and will not be improved by increases in network resolution.

[2] P. S. Dodds and D. H. Rothman.
``Scaling, universality, and geomorphology,''
Annual Review of Earth and Planetary Sciences, 28, 571-610, 2000.
# Times Cited: 59
[download reprint]
Abstract
Theories of scaling apply wherever there is similarity across many scales. This similarity may be found in geometry and in dynamical processes. Universality arises when the qualitative character of a system is sufficient to quantitatively specify its essential features, such as the exponents that characterize scaling laws. Within geomorphology, two areas where the concepts of scaling and universality have found application are the geometry of river networks and the statistical structure of topography. We first provide a pedagogical review of scaling and universality. We then describe recent progress made in applying these ideas to networks and topography. This overview then leads to a synthesis of some widely scattered ideas that attempts a classification of surface and network properties based on generic mechanisms and geometric constraints. We also briefly review how these ideas may be applied to problems in sedimentology ranging from the structure of submarine canyons, the size distribution of turbidite deposits, and the origin of stromatolites.

[1] P. S. Dodds and D. H. Rothman.
``Unified view of scaling laws for river networks,''
Physical Review E 59(5), 4865-4877, 1999.
# Times Cited: 49
[download reprint]
Abstract
Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are: (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland flow into channels occurs over a characteristic distance (drainage density is uniform). We obtain a complete set of scaling relations connecting the exponents of these scaling laws and find that only two of these exponents are independent. We further demonstrate that the two predominant descriptions of network structure (Tokunaga's law and Horton's laws) are equivalent in the case of landscapes with uniform drainage density. The results are tested with data from both real landscapes and a special class of random networks.