Publications
2013
Unique in the Crowd: The privacy bounds of human mobility. Scientific Reports (March 2013)
Abstract:
We study fifteen months of human mobility data for one and a half million individuals and find that human mobility traces are highly unique. In fact, in a dataset where the location of an individual is specified hourly, and with a spatial resolution equal to that given by the carrier’s antennas, four spatio-temporal points are enough to uniquely identify 95% of the individuals. We coarsen the data spatially and temporally to find a formula for the uniqueness of human mobility traces given their resolution and the available outside information. This formula shows that the uniqueness of mobility traces decays approximately as the 1/10 power of their resolution. Hence, even coarse datasets provide little anonymity. These findings represent fundamental constraints to an individual’s privacy and have important implications for the design of frameworks and institutions dedicated to protect the privacy of individuals.
The Structure and Dynamics of International Development Assistance. Journal of Globalization and Development (March 2013)
Abstract:
We study the structure of international aid coordination by creating and analyzing a tripartite network of donor organizations, recipient countries and development issues using web-based information. We develop a measure of coordination and find that it is moderate, achieving about 60% of its theoretical maximum. Many countries are strongly connected to organizations that are related to the issues that are salient there. Nevertheless, we identify many countries that are poorly served, issues that are inadequately attended to, and organizations that focus on the wrong combination of places and issues. Our approach may be used to improve decentralized coordination.
2012
Place Pulse: Measuring the collaborative image of the city
Abstract:
This thesis presents Place Pulse, a tool capable of conducting large crowdsourced visual preference surveys. The data collected with Place Pulse was used to create quantitaive measures of the perceptions people hold of urban environments. From this data, novel algorithms identified locations associated with positive and negative perceptions of safety, social class and uniqueness. The high throughput of the tool addressed two important methodological questions: the number of responses required to obtain robust results in a comparative study, and the number of images required to get a statistically significant evaluative map of a large city. In clossing, the validated dataset was used to correlate perceptions of safety and social class to rates of both violent crime and high school graduation.
The Observatory: Designing Data-Driven Decision Making Tools
Abstract:
Creative usage of graphic to encode information date back to at least the beginnings of the industrial revolution. It is also around that same time that a gap between the wealthiest of nations and least begins to develop. How can we use techniques of visualization complimented with vast amounts of data to provide a lens by which we may understand economic development?
The amount of computing power and data available at our finger tips is increasing everyday. This thesis will introduce The Observatory as a tool that combines big data with interactive visualizations as a means for discerning the patterns found in economic development over the past 50 years The tool draws on influences from other interactive visualizations tools as well as theory and literature from the field of complexity economics. The impact of this tool has already begun to emerge with its proliferation online and usage by experts in the field of development economics.
Going Beyond The One-Bit Democracy. Wired UK. (November 2012)
Abstract:
Would democracy be any different if Benjamin Franklin, Thomas Jefferson and John Adams had foreseen the possibility of direct online participation? Would they have paved the way for new technologies? Or would they have built roadblocks to prevent the emergence of these new technological vehicles?
As with most historical hypotheticals, we will never know. We are in 2012, however, and despite the Internet, most countries are still stuck in one-bit democracies, where people are required to choose between two choices every four to six years.
People in the Zetttabyte age, however, is not thrilled with the outcomes of one-bit democracies. In the US, the Pew Research Center indicates that national satisfaction is only 31%, and has been below 40% for a decade. In Chile, CEP reports that 47% of the population does not feel identified with either the left, right or center. The list goes on.
But who could blame people for their discontent? One-bit democracies have important limitations, including their requirement to choose candidates, rather than issues. This focuses the little bandwidth available in a political system on candidates’ personas, rather than on relevant issues…(download article to read more)
WEF Africa 2012: The Observatory of Economic Complexity. This is Africa (2012)
Abstract:
Insensitivity of development advice to a country’s context is a fundamental criticism against the socalled Washington Consensus. This coarseness is reflected in concepts – openness to trade, governance, institutions, intermediate inputs or education – that we have come to believe as real. Yet they are abstractions that hide away complexity and might be blind to the contextspecific structure that underpins people’s ability to generate prosperity. Thinking about international development through aggregate terms might be no better than trying to understand biological organisms as mixes of water, proteins, lipids and nucleic acids. Ultimately, to understand problems of organised complexity we need to develop perspectives that look at these problems with a “genetic” resolution. Most of the tools available, however, do not have that resolution or even attempt to provide it.
During recent years we have found that detailed data on the mix of products that countries export provides a high resolution picture of a country’s economy. No two countries export the same mix of goods, and hence the goods that are associated with each country provide a unique fingerprint, a phenotype, that contains valuable information of a country’s productive genotype… (download article to read more)
Proto-genes and de novo gene birth. Nature (2012)
Abstract:
Novel protein-coding genes can arise either through re-organization of pre-existing genes or de novo1, 2. Processes involving re-organization of pre-existing genes, notably after gene duplication, have been extensively described1, 2. In contrast, de novo gene birth remains poorly understood, mainly because translation of sequences devoid of genes, or ‘non-genic’ sequences, is expected to produce insignificant polypeptides rather than proteins with specific biological functions1, 3, 4, 5, 6. Here we formalize an evolutionary model according to which functional genes evolve de novo through transitory proto-genes4 generated by widespread translational activity in non-genic sequences. Testing this model at the genome scale in Saccharomyces cerevisiae, we detect translation of hundreds of short species-specific open reading frames (ORFs) located in non-genic sequences. These translation events seem to provide adaptive potential7, as suggested by their differential regulation upon stress and by signatures of retention by natural selection. In line with our model, we establish that S. cerevisiae ORFs can be placed within an evolutionary continuum ranging from non-genic sequences to genes. We identify ~1,900 candidate proto-genes among S. cerevisiae ORFs and find that de novo gene birth from such a reservoir may be more prevalent than sporadic gene duplication. Our work illustrates that evolution exploits seemingly dispensable sequences to generate adaptive functional innovation.
The Dynamics of Nestedness Predicts the Evolution of Industrial Ecosystems, PLOS ONE (2012)
Abstract:
In economic systems, the mix of products that countries make or export has been shown to be a strong leading indicator of economic growth. Hence, methods to characterize and predict the structure of the network connecting countries to the products that they export are relevant for understanding the dynamics of economic development. Here we study the presence and absence of industries at the global and national levels and show that these networks are significantly nested. This means that the less filled rows and columns of these networks’ adjacency matrices tend to be subsets of the fuller rows and columns. Moreover, we show that nestedness remains relatively stable as the matrices become more filled over time and that this occurs because of a bias for industries that deviate from the networks’ nestedness to disappear, and a bias for the missing industries that reduce nestedness to appear. This makes the appearance and disappearance of individual industries in each location predictable. We interpret the high level of nestedness observed in these networks in the context of the neutral model of development introduced by Hidalgo and Hausmann (2009). We show that, for the observed fills, the model can reproduce the high level of nestedness observed in these networks only when we assume a high level of heterogeneity in the distribution of capabilities available in countries and required by products. In the context of the neutral model, this implies that the high level of nestedness observed in these economic networks emerges as a combination of both, the complementarity of inputs and heterogeneity in the number of capabilities available in countries and required by products. The stability of nestedness in industrial ecosystems, and the predictability implied by it, demonstrates the importance of the study of network properties in the evolution of economic networks.
International Knowledge Diffusion and the Comparative Advantage of Nations. CID Working Paper 235 (2012)
Under Submission (2012) Authors: D Bahar, R Hausmann, CA Hidalgo
Abstract:
In this paper we document that the probability that a product is added to a country’s export basket is, on average, 65% larger if a neighboring country is a successful exporter of that same product. We interpret our result as evidence of international intra-industry knowledge diffusion. Our results are consistent with the overall consensus in the literature on technology spillovers: diffusion is stronger at shorter distances; is weaker for more knowledge-intensive products; and has become faster over time.
2011
The Atlas of Economic Complexity. Puritan Press (2012)
Puritan Press, Cambridge MA (2011)ISBN-10: 0615546625 ISBN-13: 9780615546629 Authors: R. Hausmann, CA Hidalgo, S Bustos, M Coscia, S Chung, J Jimenez, A Simoes, M.A. Yildirim
Abstract:
This book summarizes our work in networks and economic development, introduces the concept of personbyte, and provides growth predictions for the year 2020.
The Network Structure of Economic Output. Journal of Economic Growth (2011)
Journal of Economic Growth (2011) 16:309-342 Authors: R Hausmann, CA Hidalgo
Abstract:
Much of the analysis of economic growth has focused on the study of aggregate output. Here, we deviate from this tradition and look instead at the structure of output embodied in the network connecting countries to the products that they export.We characterize this network using four structural features: the negative relationship between the diversification of a country and the average ubiquity of its exports, and the non-normal distributions for product ubiquity, country diversification and product co-export. We model the structure of the network by assuming that products require a large number of non-tradable inputs, or capabilities, and that countries differ in the completeness of the set of capabilities they have. We solve the model assuming that the probability that a country has a capability and that a product requires a capability are constant and calibrate it to the data to find that it accounts well for all of the network features except for the heterogeneity in the distribution of country diversification. In the light of the model, this is evidence of a large heterogeneity in the distribution of capabilities across countries. Finally, we show that the model implies that the increase in diversification that is expected from the accumulation of a small number of capabilities is small for countries that have a few of them and large for those with many. This implies that the forces that help drive divergence in product diversity increase with the complexity of the global economy when capabilities travel poorly.
Discovering Southern and East Africa's Industrial Opportunities. German Marshall Fund Policy Paper Series (2011)
German Marshall Fund, Economic Policy Paper Series (2011) Author: CA Hidalgo
Abstract:
What are Southern and East Africa’s industrial opportunities? In this article the author explores this question by using the product space to study the productive structure of five Southern and East African countries: Kenya, Mozambique, Rwanda, Tanzania, and Zambia. The product space is a network connecting products that tend to be exported by the same sets of countries. Since countries are more likely to develop products that are close by in the product space to the ones that they already produce, the product space can be used to help anticipate a country’s industrial opportunities.
The results suggest that the most natural avenue for future product diversification for these five Southern and East African nations resides in the agricultural sector, since all of these nations appear to have productive structures that are pre-adapted to the production of many agricultural products that none of them are currently exporting.
The author concludes this paper by exploring the potential benefits of further regional economic integration through an exercise in which he pulled together the productive structures of these five countries. This exercise shows that the products that become more accessible in the combined economy are once again predominantly agricultural. These results suggest that while diversification into all sectors should remain an important long-term goal of the region, the path towards increased diversification in the near future may well lie in a more empowered and diverse agricultural sector.
The value in the links: networks and the evolution of organizations. Chapter 32 in the Sage Handbook on Management and Complexity (2011)
2010
Country Diversity, Product Ubiquity and Economic Divergence. CID Working Paper (2010)
CID Working Paper 201 (2010). Published as The Network Structure of Economic Output (2011) Authors: R. Hausmann, CA Hidalgo
Abstract:
Countries differ markedly in the diversification of their exports. Products differ in the number of countries that export them, which we define as their ubiquity. We document a new stylized fact in the global pattern of exports: there is a systematic relationship between the diversification of a country’s exports and the ubiquity of its products. We argue that this fact is not implied by current theories of international trade and show that it is not a trivial consequence of the heterogeneity in the level of diversification of countries or of the heterogeneity in the ubiquity of products. We account for this stylized fact by constructing a simple model that assumes that each product requires a potentially large number of non-tradable inputs, which we call capabilities, and that a country can only make the products for which it has all the requisite capabilities. Products differ in the number and specific nature of the capabilities they require, as countries differ in the number/nature of capabilities they have. Products that require more capabilities will be accessible to fewer countries (i.e., will be less ubiquitous), while countries that have more capabilities will have what is required to make more products (i.e., will be more diversified). Our model implies that the return to the accumulation of new capabilities increases exponentially with the number of capabilities already available in a country. Moreover, we find that the convexity of the increase in diversification associated with the accumulation of a new capability increases when either the total number of capabilities that exist in the world increases or the average complexity of products, defined as the number of capabilities products require, increases. This convexity defines what we term as a quiescence trap, or a trap of economic stasis: countries with few capabilities will have negligible or no return to the accumulation of more capabilities, while at the same time countries with many capabilities will experience large returns – in terms of increased diversification – to the accumulation of additional capabilities. We calibrate the model to three different sets of empirical data and show that the derived functional forms reproduce the empirically observed distributions of product ubiquity, the relationship between the diversification of countries and the average ubiquity of the products they export, and the distribution of the probability that two products are co-exported. This calibration suggests that the global economy is composed of a relatively large number of capabilities – between 23 and 80, depending on the level of disaggregation of the data – and that products require on average a relatively large fraction of these capabilities in order to be produced. The conclusion of this calibration is that the world exists in a regime where the quiescence trap is strong.
Graphical Statistical Methods for the Representation of the Human Development Index and its Components. Human Development Research Paper, United Nations (2010)
Human Development Research Paper 2010/39 (2010) Author: CA Hidalgo
Abstract:
In this paper we introduce five graphical statistical methods to compare countries level of development relative to other countries and across time. For this, we use seven panels of data on the Human Development Index and its components, containing information on more than 100 countries for more than 35 years. We create visual comparisons of the level of development of countries relative to each other, and across time, through five different visualization techniques: (i) Rankings (ii) Values (iii) Distributions (iv) visual metaphors (The Development Tree), and (v) networks, by introducing the concepts of Partial Ordering Networks (PON) and Development Reference Groups (DRG).
The graphical exploration of both, values and distributions, show a saturation of both the education and life dimensions of the HDI, suggesting a need to extend the definitions of this components to include either more subcomponents, or completely new measures that could help differentiate between countries facing different development challenges. The Development Tree and the Partial Ordering Network, on the other hand, are used to create graphical narratives of countries and regions. The simplicity of the Development Tree makes it an ideal graphical metaphor for branding the HDI in a multilingual setting, whereas Partial Ordering Networks provide a more organic way to group countries according to their levels of development and connect countries to those with similar development challenges. We conclude by arguing that graphical statistical methods could be used to help communicate complex data and concepts through universal cognitive channels that are heretofore underused in the development literature.
The Dynamics of Economic Complexity and the Product Space over a 42 year period - CID Working Paper (2010)
CID Working Paper 189 (2010) Author: CA Hidalgo.
Abstract:
How does the productive structure of countries’ changes over time? In this paper we explore this question by combining techniques of networks science with 42 years of trade data and find that, while the Product Space remains relatively stable during this period, the dynamics of countries’ productive structures is characterized by a few highly dynamic economies. In particular we identify Brazil, Indonesia, Turkey, Malaysia, Thailand, Korea, Singapore and China, as countries that transformed their productive structures considerably during these four decades, albeit following different trajectories. For instance, the economic complexity of Korea, Singapore and China was relatively high at the beginning of the observation period and continued to increase during these forty two years, moving these countries into the top spots of the economic complexity rankings for the beginning of this millennium. Brazil, Indonesia and Turkey, on the other hand, transformed their productive structures significantly during the same period of time, but did so starting from a less sophisticated foundation. We conclude the paper by moving from this and other observations into the policy implications of this view of economic development and argue that the government involvement in the private sector should be to help catalyze market activities and solve coordination problems that emerge naturally when countries try to accumulate capabilities. This represents an alternative to more traditional views of the role of government that postulate, in their extremes, that the public sector should either have no involvement in private sector activities or, on the other hand, substantial ownership of the means of production.
2009
The Building Blocks of Economic Complexity. PNAS (2009)
Proc. Natl. Acad. Sci. (2009) 106(26):10570-10575 Authors: CA Hidalgo, R Hausmann
Abstract:
For Adam Smith, wealth was related to the division of labor. As people and firms specialize in different activities, economic efficiency increases, suggesting that development is associated with an increase in the number of individual activities and with the complexity that emerges from the interactions between them. Here we develop a view of economic growth and development that gives a central role to the complexity of a country’s economy by interpreting trade data as a bipartite network in which countries are connected to the products they export, and show that it is possible to quantify the complexity of a country’s economy by characterizing the structure of this network. Furthermore, we show that the measures of complexity we derive are correlated with a country’s level of income, and that deviations from this relationship are predictive of future growth. This suggests that countries tend to converge to the level of income dictated by the complexity of their productive structures, indicating that development efforts should focus on generating the conditions that would allow complexity to emerge to generate sustained growth and prosperity.
Understanding the spread of Mobile Phone Viruses. Science (2009)
Science (2009) 324:1071-1076 Authors: P Wang, MC Gonzalez, CA Hidalgo, A-L Barabasi
Abstract:
We modeled the mobility of mobile phone users in order to study the fundamental spreading patterns that characterize a mobile virus outbreak. We find that although Bluetooth viruses can reach all susceptible handsets with time, they spread slowly because of human mobility, offering ample opportunities to deploy antiviral software. In contrast, viruses using multimedia messaging services could infect all users in hours, but currently a phase transition on the underlying call graph limits them to only a small fraction of the susceptible users. These results explain the lack of a major mobile virus breakout so far and predict that once a mobile operating system’s market share reaches the phase transition point, viruses will pose a serious threat to mobile communications.
A Dynamic Network Approach for the study of human phenotypes - PLOS Computational Biology (2009)
PLoS Computational Biology (2009) 5(4):e1000353 doi:10.1371/journal.pcbi.1000353 Authors CA Hidalgo, N Blumm, A-L Barabasi, NA Christakis.
Abstract:
The use of networks to integrate different genetic, proteomic, and metabolic datasets has been proposed as a viable path toward elucidating the origins of specific diseases. Here we introduce a new phenotypic database summarizing correlations obtained from the disease history of more than 30 million patients in a Phenotypic Disease Network (PDN). We present evidence that the structure of the PDN is relevant to the understanding of illness progression by showing that (1) patients develop diseases close in the network to those they already have; (2) the progression of disease along the links of the network is different for patients of different genders and ethnicities; (3) patients diagnosed with diseases which are more highly connected in the PDN tend to die sooner than those affected by less connected diseases; and (4) diseases that tend to be preceded by others in the PDN tend to be more connected than diseases that precede other illnesses, and are associated with higher degrees of mortality. Our findings show that disease progression can be represented and studied using network methods, offering the potential to enhance our understanding of the origin and evolution of human diseases. The dataset introduced here, released concurrently with this publication, represents the largest relational phenotypic resource publicly available to the research community.
2008
Thinking Outside the Cube. PhysicsWorld (2008)
A Network View of Economic Development. Developing Alternatives (2008)
Developing Alternatives (2008) 12(1): 5-10 Authors: CA Hidalgo, R Hausmann
Abstract:
Does the type of product a country exports matter for subsequent economic performance? to take an example from the 19th-century economist David Ricardo, does it matter if Britain specializes in cloth and portugal in wine for the subsequent development of either country? the seminal texts of development economics held that it does matter, suggesting that industrialization creates externalities that lead to accelerated growth (rosenstein-rodan 1943; Hirschman 1958; Matsuyama 1992). Yet, lacking formal models, mainstream economic theory has made little of these ideas. instead, current dominant theories use two approaches to explain countries’ patterns of specialization. The first approach focuses on the relative proportions in which countries possess productive factors (physical capital, labor, land, skills or human capital, infrastructure, and institutions) and the proportions in which these factors are needed to produce different goods (see Flam and Flanders 1991). Hence, poor countries specialize in goods that are relatively intensive in labor and land, while richer countries specialize in goods that use more human and physical capital and demand better infrastructure and institutions. According to these… (read more by downloading paper)
Understanding Individual Human Mobility Patterns. Nature (2008)
Nature (2008) 453: 779-782 Authors: MC Gonzalez, CA Hidalgo, A-L Barabasi
Abstract:
Despite their importance for urban planning, traffic forecasting, and the spread of biological and mobile viruses, our understanding of the basic laws governing human motion remains limited owing to the lack of tools to monitor the time-resolved location of individuals. Here we study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six-month period. We find that, in contrast with the random trajectories predicted by the prevailing Le´vy flight and random walk models, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a timeindependent characteristic travel distance and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that, despite the diversity of their travel history, humans follow simple reproducible patterns. This inherent similarity in travel patterns could impact all phenomena driven by human mobility, from epidemic prevention to emergency response, urban planning and agent-based modelling.
The Dynamics of a Mobile Phone Network. Physica A (2008)
Physica A (2008), 387(12): 3017-3024 Authors: CA Hidalgo, C Rodriguez-Sickert
Abstract:
The empirical study of network dynamics has been limited by the lack of longitudinal data. Here we introduce a quantitative indicator of link persistence to explore the correlations between the structure of a mobile phone network and the persistence of its links.We show that persistent links tend to be reciprocal and are more common for people with low degree and high clustering. We study the redundancy of the associations between persistence, degree, clustering and reciprocity and show that reciprocity is the strongest predictor of tie persistence. The method presented can be easily adapted to characterize the dynamics of other networks and can be used to identify the links that are most likely to survive in the future
2007
The Product Space Conditions the Development of Nations. Science (2007)
Science (2007) 317: 482-487 Authors: CA Hidalgo, B Klinger, A-L Barabasi, R Hausmann
Abstract:
Economies grow by upgrading the products they produce and export. The technology, capital, institutions, and skills needed to make newer products are more easily adapted from some products than from others. Here, we study this network of relatedness between products, or “product space,” finding that more-sophisticated products are located in a densely connected core whereas less sophisticated products occupy a less-connected periphery. Empirically, countries move through the product space by developing goods close to those they currently produce. Most countries can reach the core only by traversing empirically infrequent distances, which may help explain why poor countries have trouble developing more competitive exports and fail to converge to the income levels of rich countries.
Transcription Factor Modularity in a Gene-Centered C. elegans Protein-DNA Interaction Network. Genome Research (2007)
Genome Research (2007) 17:1061-1071 Authors:V Vermeirssen, MI Barrasa, CA Hidalgo et al.
Abstract:
Transcription regulatory networks play a pivotal role in the development, function, and pathology of metazoan organisms. Such networks are comprised of protein–DNA interactions between transcription factors (TFs) and their target genes. An important question pertains to how the architecture of such networks relates to network functionality. Here, we show that a Caenorhabditis elegans core neuronal protein–DNA interaction network is organized into two TF modules. These modules contain TFs that bind to a relatively small number of target genes and are more systems specific than the TF hubs that connect the modules. Each module relates to different functional aspects of the network. One module contains TFs involved in reproduction and target genes that are expressed in neurons as well as in other tissues. The second module is enriched for paired homeodomain TFs and connects to target genes that are often exclusively neuronal. We find that paired homeodomain TFs are specifically expressed in C. elegans and mouse neurons, indicating that the neuronal function of paired homeodomains is evolutionarily conserved. Taken together, we show that a core neuronal C. elegans protein–DNA interaction network possesses TF modules that relate to different functional aspects of the complete network.
Genome-scale analysis of in vivo spatiotemporal promoter activity in C. elegans. Nature Biotechnology (2007)
Nature Biotechnology 25, 663 – 668 (2007) Authors: D Dupuy, N Bertin, CA Hidalgo et al.
Abstract:
Differential regulation of gene expression is essential for cell fate specification in metazoans. Characterizing the transcriptional activity of gene promoters, in time and in space, is therefore a critical step toward understanding complex biological systems. Here we present an in vivo spatiotemporal analysis for B900 predicted C. elegans promoters (B5% of the predicted proteincoding genes), each driving the expression of green fluorescent protein (GFP). Using a flow-cytometer adapted for nematode profiling, we generated ‘chronograms’, two-dimensional representations of fluorescence intensity along the body axis and throughout development from early larvae to adults. Automated comparison and clustering of the obtained in vivo expression patterns show that genes coexpressed in space and time tend to belong to common functional categories. Moreover, integration of this data set with C. elegans protein-protein interactome data sets enables prediction of anatomical and temporal interaction territories between protein partners.
2006
The effect of social interactions in the primary life cycle of motion pictures. New Journal of Physics (2006)
New J. Phys. 8 52 (2006) Authors: CA Hidalgo, C Rodriguez-Sickert.
Abstract:
We develop a ‘basic principles’modelwhich accounts for the primary life cycle consumption of films as a social coordination problem in which information transmission is governed by word of mouth. We fit the analytical solution of such a model to aggregated consumption data from the film industry and derive a quantitative estimator of its quality based on the structure of the life cycle.
Conditions for the Emergence of Scaling in the Inter-Event Time of Uncorrelated and Seasonal Systems.
Physica A. Vol. 369(2) p 877-883. (2006) Authors: CA Hidalgo.
Abstract:
Inter-event times have been studied across various disciplines in search for correlations. In this paper, we show analytical and numerical evidence that at the population level a power-law can be obtained by assuming Poissonian agents with different characteristic times, and at the individual level by assuming Poissonian agents that change the rates at which they perform an event in a random or deterministic fashion. The range in which we expect to see this behavior and the possible deviations from it are studied by considering the shape of the rate distribution.
2005
Stationary States of a Random Copying Mechanism over a Complex Networks. Physica A (2005)
Physica A, (2005) 353:674-684 Authors: CA Hidalgo, PA Marquet, F Claro.
Abstract:
An analytical approach to network dynamics is used to show that when agents copy their state randomly, the network arrives to a stationary regime in which the distribution of states is independent of the degree. The effects of network topology on the process are characterized introducing a quantity called influence and studying its behavior for scale-free and random networks. We show that for this model degree averaged quantities are constant in time regardless of the number of states involved.