Opinion formation driven by PageRank node influence on directed networks

We study a two states opinion formation model driven by PageRank node influence and report an extensive numerical study on how PageRank affects collective opinion formations in large-scale empirical directed networks. In our model the opinion of a node can be updated by the sum of its neighbor nodes' opinions weighted by the node influence of the neighbor nodes at each step. We consider PageRank probability and its sublinear power as node influence measures and investigate evolution of opinion under various conditions. First, we observe that all networks reach steady state opinion after a certain relaxation time. This time scale is decreasing with the heterogeneity of node influence in the networks. Second, we find that our model shows consensus and non-consensus behavior in steady state depending on types of networks: Web graph, citation network of physics articles, and LiveJournal social network show non-consensus behavior while Wikipedia article network shows consensus behavior. Third, we find that a more heterogeneous influence distribution leads to a more uniform opinion state in the cases of Web graph, Wikipedia, and Livejournal. However, the opposite behavior is observed in the citation network. Finally we identify that a small number of influential nodes can impose their own opinion on significant fraction of other nodes in all considered networks. Our study shows that the effects of heterogeneity of node influence on opinion formation can be significant and suggests further investigations on the interplay between node influence and collective opinion in networks.Comment: 10 pages, 6 figures. Published in Physica A 436, 707-715 (2015

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.Comment: Published in PLoS ONE (http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0074554). Supporting information is available on the same webpag

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.Comment: Published in Scientific Report

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 allows to resolve hard numerical problems for small eigenvalues. The nearly nilpotent matrix structure allows to obtain a semi-analytical computation of eigenvalues. We find that the spectrum is characterized by the fractal Weyl law with a fractal dimension $d_f \approx 1$. 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.Comment: 25 pages. 17 figures. Published in Phys. Rev.

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.Comment: 9 pages, 6 figure

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

Credit Risk and the Pricing of Japanese Yen Interest Rate Swaps

In this paper, we investigate the pricing of Japanese yen interest rate swaps during the period 1990-96. We obtain measures of the spreads of the swap rates over comparable Japanese Government Bonds (JGBs) for different maturities and analyze the relationship between the swap spreads and credit risk variables

Credit Risk and the Yen Interest Rate Swap Market

In this paper, we investigate the pricing of Japanese yen interest rate swaps during the period 1990-96. We obtain measures of the spreads of the swap rates over comparable Japanese Government Bonds (JGBs) for di erent maturities and analyze the relationship between the swap spreads and credit risk variables. Our empirical results in the yen swap market indicate that: 1) the commonly-used as- sumption of lognormal default-free interest rates and swap spreads is strongly rejected by the data, 2) the term structure of swap spreads displays a humped-shape, and 3) the shocks in the yen swap spread are negatively correlated with the shocks in the comparable default-free spot rates, especially for longer maturities. Our analysis also indicates that yen swap spreads behaved very di erently from the credit spreads on Japanese corporate bonds in the early nineties. In contrast to Japanese corporate bonds, we find that the yen swap spread is also significantly related to proxies for the longterm credit risk factor. Furthermore, the swap spread is negatively related to the level and slope of the term structure and positively related to the curvature, indicating that the credit \optionality" is priced in the swap rate. Thus, overall, the yen swap market was sensitive to credit risk during the period of our study

Credit Risk and the Yen Interest Rate Swap Market

In this paper, we investigate the pricing of Japanese yen interest rate swaps during the period 1990-96. We obtain measures of the spreads of the swap rates over comparable Japanese Government Bonds (JGBs) for different maturities and analyze the relationship between the swap spreads and credit risk variables. Our empirical results in the yen swap market indicate that: 1) the commonly-used assumption of lognormal default-free interest rates and swap spreads is strongly rejected by the data, 2) the term structure of swap spreads displays a humped-shape, and 3) the shocks in the yen swap spread are negatively correlated with the shocks in the comparable default-free spot rates, especially for longer maturities. Our analysis also indicates that yen swap spreads behaved very differently from the credit spreads on Japanese corporate bonds in the early nineties. In contrast to Japanese corporate bonds, we find that the yen swap spread is also significantly related to proxies for the long-term credit risk factor. Furthermore, the swap spread is negatively related to the level and slope of the term structure and positively related to the curvature, indicating that the credit "optionality" is priced in the swap rate. Thus, overall, the yen swap market was sensitive to credit risk during the period of our study