Empirical analysis of congestion spreading in Seoul traffic network.

Understanding how local traffic congestion spreads in urban traffic networks is fundamental to solving congestion problems in cities. In this work, by analyzing the high-resolution data of traffic velocity in Seoul, we empirically investigate the spreading patterns and cluster formation of traffic congestion in a real-world urban traffic network. To do this, we propose a congestion identification method suitable for various types of interacting traffic flows in urban traffic networks. Our method reveals that congestion spreading in Seoul may be characterized by a treelike structure during the morning rush hour but a more persistent loop structure during the evening rush hour. Our findings suggest that diffusion and stacking processes of local congestion play a major role in the formation of urban traffic congestion.

Global efficiency and network structure of urban traffic flows: A percolation-based empirical analysis.

Making the connection between the function and structure of networked systems is one of the fundamental issues in complex systems and network science. Urban traffic flows are related to various problems in cities and can be represented as a network of local traffic flows. To identify an empirical relation between the function and network structure of urban traffic flows, we construct a time-varying traffic flow network of a megacity, Seoul, and analyze its global efficiency with a percolation-based approach. Comparing the real-world traffic flow network with its corresponding null-model network having a randomized structure, we show that the real-world network is less efficient than its null-model network during rush hour, yet more efficient during non-rush hour. We observe that in the real-world network, links with the highest betweenness tend to have lower quality during rush hour compared to links with lower betweenness, but higher quality during non-rush hour. Since the top betweenness links tend to be the bridges that connect the network together, their congestion has a stronger impact on the network's global efficiency. Our results suggest that the spatial structure of traffic flow networks is important to understand their function.

Copula-based analysis of the generalized friendship paradox in clustered networks.

A heterogeneous structure of social networks induces various intriguing phenomena. One of them is the friendship paradox, which states that on average, your friends have more friends than you do. Its generalization, called the generalized friendship paradox (GFP), states that on average, your friends have higher attributes than yours. Despite successful demonstrations of the GFP by empirical analyses and numerical simulations, analytical, rigorous understanding of the GFP has been largely unexplored. Recently, an analytical solution for the probability that the GFP holds for an individual in a network with correlated attributes was obtained using the copula method but by assuming a locally tree structure of the underlying network [Jo et al., Phys. Rev. E 104, 054301 (2021)]. Considering the abundant triangles in most social networks, we employ a vine copula method to incorporate the attribute correlation structure between neighbors of a focal individual in addition to the correlation between the focal individual and its neighbors. Our analytical approach helps us rigorously understand the GFP in more general networks, such as clustered networks and other related interesting phenomena in social networks.

Analytical approach to the generalized friendship paradox in networks with correlated attributes.

One of the interesting phenomena due to the topological heterogeneities in complex networks is the friendship paradox, stating that your friends have on average more friends than you do. Recently, this paradox has been generalized for arbitrary nodal attributes, called a generalized friendship paradox (GFP). In this paper, we analyze the GFP for the networks in which the attributes of neighboring nodes are correlated with each other. The correlation structure between attributes of neighboring nodes is modeled by the Farlie-Gumbel-Morgenstern copula, enabling us to derive approximate analytical solutions of the GFP for three kinds of methods summarizing the neighborhood of the focal node, i.e., mean-based, median-based, and fraction-based methods. The analytical solutions are comparable to simulation results, while some systematic deviations between them might be attributed to the higher-order correlations between nodal attributes. These results help us get deeper insight into how various summarization methods as well as the correlation structure of nodal attributes affect the GFP behavior, hence better understand various related phenomena in complex networks.

Impact of perception models on friendship paradox and opinion formation.

Topological heterogeneities of social networks have a strong impact on the individuals embedded in those networks. One of the interesting phenomena driven by such heterogeneities is the friendship paradox (FP), stating that the mean degree of one's neighbors is larger than the degree of oneself. Alternatively, one can use the median degree of neighbors as well as the fraction of neighbors having a higher degree than oneself. Each of these reflects on how people perceive their neighborhoods, i.e., their perception models, hence how they feel peer pressure. In our paper, we study the impact of perception models on the FP by comparing three versions of the perception model in networks generated with a given degree distribution and a tunable degree-degree correlation or assortativity. The increasing assortativity is expected to decrease network-level peer pressure, while we find a nontrivial behavior only for the mean-based perception model. By simulating opinion formation, in which the opinion adoption probability of an individual is given as a function of individual peer pressure, we find that it takes the longest time to reach consensus when individuals adopt the median-based perception model compared to other versions. Our findings suggest that one needs to consider the proper perception model for better modeling human behaviors and social dynamics.

Resilience of networks to environmental stress: From regular to random networks.

Despite the huge interest in network resilience to stress, most of the studies have concentrated on internal stress damaging network structure (e.g., node removals). Here we study how networks respond to environmental stress deteriorating their external conditions. We show that, when regular networks gradually disintegrate as environmental stress increases, disordered networks can suddenly collapse at critical stress with hysteresis and vulnerability to perturbations. We demonstrate that this difference results from a trade-off between node resilience and network resilience to environmental stress. The nodes in the disordered networks can suppress their collapses due to the small-world topology of the networks but eventually collapse all together in return. Our findings indicate that some real networks can be highly resilient against environmental stress to a threshold yet extremely vulnerable to the stress above the threshold because of their small-world topology.

Concurrent enhancement of percolation and synchronization in adaptive networks.

Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of connectivity, and show that it self-organizes from fragmented and incoherent states to connected and synchronized ones. The synchronization and percolation are associated to abrupt transitions, and they are concurrently (and significantly) enhanced as compared to the non-adaptive case. Finally we provide evidence that only partial adaptation is sufficient to determine these enhancements. Our study, therefore, indicates that inclusion of simple adaptive mechanisms can efficiently describe some emergent features of networked systems' collective behaviors, and suggests also self-organized ways to control synchronization and percolation in natural and social systems.

Twitter-Based Analysis of the Dynamics of Collective Attention to Political Parties.

Large-scale data from social media have a significant potential to describe complex phenomena in the real world and to anticipate collective behaviors such as information spreading and social trends. One specific case of study is represented by the collective attention to the action of political parties. Not surprisingly, researchers and stakeholders tried to correlate parties' presence on social media with their performances in elections. Despite the many efforts, results are still inconclusive since this kind of data is often very noisy and significant signals could be covered by (largely unknown) statistical fluctuations. In this paper we consider the number of tweets (tweet volume) of a party as a proxy of collective attention to the party, identify the dynamics of the volume, and show that this quantity has some information on the election outcome. We find that the distribution of the tweet volume for each party follows a log-normal distribution with a positive autocorrelation of the volume over short terms, which indicates the volume has large fluctuations of the log-normal distribution yet with a short-term tendency. Furthermore, by measuring the ratio of two consecutive daily tweet volumes, we find that the evolution of the daily volume of a party can be described by means of a geometric Brownian motion (i.e., the logarithm of the volume moves randomly with a trend). Finally, we determine the optimal period of averaging tweet volume for reducing fluctuations and extracting short-term tendencies. We conclude that the tweet volume is a good indicator of parties' success in the elections when considered over an optimal time window. Our study identifies the statistical nature of collective attention to political issues and sheds light on how to model the dynamics of collective attention in social media.

Tail-scope: Using friends to estimate heavy tails of degree distributions in large-scale complex networks.

Many complex networks in natural and social phenomena have often been characterized by heavy-tailed degree distributions. However, due to rapidly growing size of network data and concerns on privacy issues about using these data, it becomes more difficult to analyze complete data sets. Thus, it is crucial to devise effective and efficient estimation methods for heavy tails of degree distributions in large-scale networks only using local information of a small fraction of sampled nodes. Here we propose a tail-scope method based on local observational bias of the friendship paradox. We show that the tail-scope method outperforms the uniform node sampling for estimating heavy tails of degree distributions, while the opposite tendency is observed in the range of small degrees. In order to take advantages of both sampling methods, we devise the hybrid method that successfully recovers the whole range of degree distributions. Our tail-scope method shows how structural heterogeneities of large-scale complex networks can be used to effectively reveal the network structure only with limited local information.

Interactions of cultures and top people of Wikipedia from ranking of 24 language editions.

Wikipedia is a huge global repository of human knowledge that can be leveraged to investigate interwinements between cultures. With this aim, we apply methods of Markov chains and Google matrix for the analysis of the hyperlink networks of 24 Wikipedia language editions, and rank all their articles by PageRank, 2DRank and CheiRank algorithms. Using automatic extraction of people names, we obtain the top 100 historical figures, for each edition and for each algorithm. We investigate their spatial, temporal, and gender distributions in dependence of their cultural origins. Our study demonstrates not only the existence of skewness with local figures, mainly recognized only in their own cultures, but also the existence of global historical figures appearing in a large number of editions. By determining the birth time and place of these persons, we perform an analysis of the evolution of such figures through 35 centuries of human history for each language, thus recovering interactions and entanglement of cultures over time. We also obtain the distributions of historical figures over world countries, highlighting geographical aspects of cross-cultural links. Considering historical figures who appear in multiple editions as interactions between cultures, we construct a network of cultures and identify the most influential cultures according to this network.

Network-based model of the growth of termite nests.

We present a model for the growth of the transportation network inside nests of the social insect subfamily Termitinae (Isoptera, termitidae). These nests consist of large chambers (nodes) connected by tunnels (edges). The model based on the empirical analysis of the real nest networks combined with pruning (edge removal, either random or weighted by betweenness centrality) and a memory effect (preferential growth from the latest added chambers) successfully predicts emergent nest properties (degree distribution, size of the largest connected component, average path lengths, backbone link ratios, and local graph redundancy). The two pruning alternatives can be associated with different genuses in the subfamily. A sensitivity analysis on the pruning and memory parameters indicates that Termitinae networks favor fast internal transportation over efficient defense strategies against ant predators. Our results provide an example of how complex network organization and efficient network properties can be generated from simple building rules based on local interactions and contribute to our understanding of the mechanisms that come into play for the formation of termite networks and of biological transportation networks in general.

Google matrix of the citation network of Physical Review.

We study the statistical properties of spectrum and eigenstates of the Google matrix of the citation network of Physical Review for the period 1893-2009. The main fraction of complex eigenvalues with largest modulus is determined numerically by different methods based on high-precision computations with up to p = 16384 binary digits that allow us to resolve hard numerical problems for small eigenvalues. The nearly nilpotent matrix structure allows us to obtain a semianalytical computation of eigenvalues. We find that the spectrum is characterized by the fractal Weyl law with a fractal dimension d(f) ≈ 1. It is found that the majority of eigenvectors are located in a localized phase. The statistical distribution of articles in the PageRank-CheiRank plane is established providing a better understanding of information flows on the network. The concept of ImpactRank is proposed to determine an influence domain of a given article. We also discuss the properties of random matrix models of Perron-Frobenius operators.

Generalized friendship paradox in networks with tunable degree-attribute correlation.

One of the interesting phenomena due to topological heterogeneities in complex networks is the friendship paradox: Your friends have on average more friends than you do. Recently, this paradox has been generalized for arbitrary node attributes, called the generalized friendship paradox (GFP). The origin of GFP at the network level has been shown to be rooted in positive correlations between degrees and attributes. However, how the GFP holds for individual nodes needs to be understood in more detail. For this, we first analyze a solvable model to characterize the paradox holding probability of nodes for the uncorrelated case. Then we numerically study the correlated model of networks with tunable degree-degree and degree-attribute correlations. In contrast to the network level, we find at the individual level that the relevance of degree-attribute correlation to the paradox holding probability may depend on whether the network is assortative or dissortative. These findings help us to understand the interplay between topological structure and node attributes in complex networks.

Generalized friendship paradox in complex networks: the case of scientific collaboration.

The friendship paradox states that your friends have on average more friends than you have. Does the paradox "hold" for other individual characteristics like income or happiness? To address this question, we generalize the friendship paradox for arbitrary node characteristics in complex networks. By analyzing two coauthorship networks of Physical Review journals and Google Scholar profiles, we find that the generalized friendship paradox (GFP) holds at the individual and network levels for various characteristics, including the number of coauthors, the number of citations, and the number of publications. The origin of the GFP is shown to be rooted in positive correlations between degree and characteristics. As a fruitful application of the GFP, we suggest effective and efficient sampling methods for identifying high characteristic nodes in large-scale networks. Our study on the GFP can shed lights on understanding the interplay between network structure and node characteristics in complex networks.

Highlighting entanglement of cultures via ranking of multilingual Wikipedia articles.

How different cultures evaluate a person? Is an important person in one culture is also important in the other culture? We address these questions via ranking of multilingual Wikipedia articles. With three ranking algorithms based on network structure of Wikipedia, we assign ranking to all articles in 9 multilingual editions of Wikipedia and investigate general ranking structure of PageRank, CheiRank and 2DRank. In particular, we focus on articles related to persons, identify top 30 persons for each rank among different editions and analyze distinctions of their distributions over activity fields such as politics, art, science, religion, sport for each edition. We find that local heroes are dominant but also global heroes exist and create an effective network representing entanglement of cultures. The Google matrix analysis of network of cultures shows signs of the Zipf law distribution. This approach allows to examine diversity and shared characteristics of knowledge organization between cultures. The developed computational, data driven approach highlights cultural interconnections in a new perspective. Dated: June 26, 2013.

Characterizing and modeling citation dynamics.

Citation distributions are crucial for the analysis and modeling of the activity of scientists. We investigated bibliometric data of papers published in journals of the American Physical Society, searching for the type of function which best describes the observed citation distributions. We used the goodness of fit with Kolmogorov-Smirnov statistics for three classes of functions: log-normal, simple power law and shifted power law. The shifted power law turns out to be the most reliable hypothesis for all citation networks we derived, which correspond to different time spans. We find that citation dynamics is characterized by bursts, usually occurring within a few years since publication of a paper, and the burst size spans several orders of magnitude. We also investigated the microscopic mechanisms for the evolution of citation networks, by proposing a linear preferential attachment with time dependent initial attractiveness. The model successfully reproduces the empirical citation distributions and accounts for the presence of citation bursts as well.

How citation boosts promote scientific paradigm shifts and nobel prizes.

Nobel Prizes are commonly seen to be among the most prestigious achievements of our times. Based on mining several million citations, we quantitatively analyze the processes driving paradigm shifts in science. We find that groundbreaking discoveries of Nobel Prize Laureates and other famous scientists are not only acknowledged by many citations of their landmark papers. Surprisingly, they also boost the citation rates of their previous publications. Given that innovations must outcompete the rich-gets-richer effect for scientific citations, it turns out that they can make their way only through citation cascades. A quantitative analysis reveals how and why they happen. Science appears to behave like a self-organized critical system, in which citation cascades of all sizes occur, from continuous scientific progress all the way up to scientific revolutions, which change the way we see our world. Measuring the "boosting effect" of landmark papers, our analysis reveals how new ideas and new players can make their way and finally triumph in a world dominated by established paradigms. The underlying "boost factor" is also useful to discover scientific breakthroughs and talents much earlier than through classical citation analysis, which by now has become a widespread method to measure scientific excellence, influencing scientific careers and the distribution of research funds. Our findings reveal patterns of collective social behavior, which are also interesting from an attention economics perspective. Understanding the origin of scientific authority may therefore ultimately help to explain how social influence comes about and why the value of goods depends so strongly on the attention they attract.

Exploring local structural organization of metabolic networks using subgraph patterns.

Metabolic networks of many cellular organisms share global statistical features. Their connectivity distributions follow the long-tailed power law and show the small-world property. In addition, their modular structures are organized in a hierarchical manner. Although the global topological organization of metabolic networks is well understood, their local structural organization is still not clear. Investigating local properties of metabolic networks is necessary to understand the nature of metabolism in living organisms. To identify the local structural organization of metabolic networks, we analysed the subgraphs of metabolic networks of 43 organisms from three domains of life. We first identified the network motifs of metabolic networks and identified the statistically significant subgraph patterns. We then compared metabolic networks from different domains and found that they have similar local structures and that the local structure of each metabolic network has its own taxonomical meaning. Organisms closer in taxonomy showed similar local structures. In addition, the common substrates of 43 metabolic networks were not randomly distributed, but were more likely to be constituents of cohesive subgraph patterns.