Heterogeneous network with distance dependent connectivity

Abstract.: We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the basic model is sharply peaked around its mean value. Since the model was originally developed to mimic the social network of acquaintances, to broaden the degree distribution we propose its generalization. We show that when heterogeneity is introduced to the model, it is possible to obtain fat tails of the degree distribution. Meanwhile, the small-world phenomenon present in the basic model is not affected. To support our claims, both analytical and numerical results are obtaine

How to project a bipartite network?

The one-mode projecting is extensively used to compress the bipartite networks. Since the one-mode projection is always less informative than the bipartite representation, a proper weighting method is required to better retain the original information. In this article, inspired by the network-based resource-allocation dynamics, we raise a weighting method, which can be directly applied in extracting the hidden information of networks, with remarkably better performance than the widely used global ranking method as well as collaborative filtering. This work not only provides a creditable method in compressing bipartite networks, but also highlights a possible way for the better solution of a long-standing challenge in modern information science: How to do personal recommendation?Comment: 7 pages, 4 figure

Recommendation model based on opinion diffusion

Information overload in the modern society calls for highly efficient recommendation algorithms. In this letter we present a novel diffusion based recommendation model, with users' ratings built into a transition matrix. To speed up computation we introduce a Green function method. The numerical tests on a benchmark database show that our prediction is superior to the standard recommendation methods.Comment: 5 pages, 2 figure

Heterogeneous network with distance dependent connectivity

We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the basic model is sharply peaked around its mean value. Since the model was originally developed to mimic the social network of acquaintances, to broaden the degree distribution we propose its generalization. We show that when heterogeneity is introduced to the model, it is possible to obtain fat tails of the degree distribution. Meanwhile, the small-world phenomenon present in the basic model is not affected. To support our claims, both analytical and numerical results are obtained.Comment: 6 pages, 4 figures, minor clarifications and references adde

Small world yields the most effective information spreading

Spreading dynamics of information and diseases are usually analyzed by using a unified framework and analogous models. In this paper, we propose a model to emphasize the essential difference between information spreading and epidemic spreading, where the memory effects, the social reinforcement and the non-redundancy of contacts are taken into account. Under certain conditions, the information spreads faster and broader in regular networks than in random networks, which to some extent supports the recent experimental observation of spreading in online society [D. Centola, Science {\bf 329}, 1194 (2010)]. At the same time, simulation result indicates that the random networks tend to be favorable for effective spreading when the network size increases. This challenges the validity of the above-mentioned experiment for large-scale systems. More significantly, we show that the spreading effectiveness can be sharply enhanced by introducing a little randomness into the regular structure, namely the small-world networks yield the most effective information spreading. Our work provides insights to the understanding of the role of local clustering in information spreading.Comment: 6 pages, 7 figures, accepted by New J. Phy

Breakdown of the mean-field approximation in a wealth distribution model

One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and M\'ezard have proposed an interesting model of economy [Bouchaud and M\'ezard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribution with a power-law tail. In this paper we examine characteristic time scales of the model and show that for any finite number of agents, the validity of the mean-field result is time-limited and the model in fact has no stationary wealth distribution. Further analysis suggests that for heterogeneous agents, the limitations are even stronger. We conclude with general implications of the presented results.Comment: 11 pages, 3 figure

Solving the apparent diversity-accuracy dilemma of recommender systems

Recommender systems use data on past user preferences to predict possible future likes and interests. A key challenge is that while the most useful individual recommendations are to be found among diverse niche objects, the most reliably accurate results are obtained by methods that recommend objects based on user or object similarity. In this paper we introduce a new algorithm specifically to address the challenge of diversity and show how it can be used to resolve this apparent dilemma when combined in an elegant hybrid with an accuracy-focused algorithm. By tuning the hybrid appropriately we are able to obtain, without relying on any semantic or context-specific information, simultaneous gains in both accuracy and diversity of recommendations.Comment: 10 pages, 9 figures, 4 tables (final version with supporting information included

General coevolution of topology and dynamics in networks

We present a general framework for the study of coevolution in dynamical systems. This phenomenon consists of the coexistence of two dynamical processes on networks of interacting elements: node state change and rewiring of links between nodes. The process of rewiring is described in terms of two basic actions: disconnection and reconnection between nodes, both based on a mechanism of comparison of their states. We assume that the process of rewiring and node state change occur with probabilities Pr and Pc respectively, independent of each other. The collective behavior of a coevolutionary system can be characterized on the space of parameters (Pr, Pc). As an application, for a voterlike node dynamics we find that reconnections between nodes with similar states lead to network fragmentation. The critical boundaries for the onset of fragmentation in networks with different properties are calculated on this space. We show that coevolution models correspond to curves on this space describing functional relations between Pr and Pc. The occurrence of a one-large-domain phase and a fragmented phase in the network is predicted for diverse models, and agreement is found with some earlier results. The collective behavior of system is also characterized on the space of parameters for the disconnection and reconnection actions. In a region of this space, we find a behavior where different node states can coexist for very long times on one large, connected network.Comment: 6 pages, 6 figure

Heterogeneity, quality, and reputation in an adaptive recommendation model

Recommender systems help people cope with the problem of information overload. A recently proposed adaptive news recommender model [Medo et al., 2009] is based on epidemic-like spreading of news in a social network. By means of agent-based simulations we study a "good get richer" feature of the model and determine which attributes are necessary for a user to play a leading role in the network. We further investigate the filtering efficiency of the model as well as its robustness against malicious and spamming behaviour. We show that incorporating user reputation in the recommendation process can substantially improve the outcome

Enhancing topology adaptation in information-sharing social networks

The advent of Internet and World Wide Web has led to unprecedent growth of the information available. People usually face the information overload by following a limited number of sources which best fit their interests. It has thus become important to address issues like who gets followed and how to allow people to discover new and better information sources. In this paper we conduct an empirical analysis on different on-line social networking sites, and draw inspiration from its results to present different source selection strategies in an adaptive model for social recommendation. We show that local search rules which enhance the typical topological features of real social communities give rise to network configurations that are globally optimal. These rules create networks which are effective in information diffusion and resemble structures resulting from real social systems