No Arabic abstract
The mechanism of the online user preference evolution is of great significance for understanding the online user behaviors and improving the quality of online services. Since users are allowed to rate on objects in many online systems, ratings can well reflect the users preference. With two benchmark datasets from online systems, we uncover the memory effect in users selecting behavior which is the sequence of qualities of selected objects and the rating behavior which is the sequence of ratings delivered by each user. Furthermore, the memory duration is presented to describe the length of a memory, which exhibits the power-law distribution, i.e., the probability of the occurring of long-duration memory is much higher than that of the random case which follows the exponential distribution. We present a preference model in which a Markovian process is utilized to describe the users selecting behavior, and the rating behavior depends on the selecting behavior. With only one parameter for each of the users selecting and rating behavior, the preference model could regenerate any duration distribution ranging from the power-law form (strong memory) to the exponential form (weak memory).
Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an analytical expression for the effect of memory on the spectral gap and thus, equivalently, on the characteristic time needed for the stochastic process to asymptotically reach equilibrium. Perturbation analysis shows that standard first-order Markov models can either overestimate or underestimate the diffusion rate of flows across the modular structure of a system captured by a second-order Markov network. We test the theoretical predictions on a toy example and on numerical data, and discuss their implications for network theory, in particular in the case of temporal or multiplex networks.
This paper is to analyze the properties of evolving bipartite networks from four aspects, the growth of networks, the degree distribution, the popularity of objects and the diversity of user behaviours, leading a deep understanding on the empirical data. By empirical studies of data from the online bookstore Amazon and a question and answer site Stack Overflow, which are both rating bipartite networks, we could reveal the rules for the evolution of bipartite networks. These rules have significant meanings in practice for maintaining the operation of real systems and preparing for their future development. We find that the degree distribution of users follows a power law with an exponential cutoff. Also, according to the evolution of popularity for objects, we find that the large-degree objects tend to receive more new ratings than expected depending on their current degrees while the small-degree objects receive less ratings in terms of their degrees. Moreover, the user behaviours show such a trend that the larger degree the users have, the stronger purposes are with their behaviours except the initial periods when users choose a diversity of products to learn about what they want. Finally, we conclude with a discussion on how the bipartite network evolves, which provides guideline for meeting challenges brought by the growth of network.
How is online social media activity structured in the geographical space? Recent studies have shown that in spite of earlier visions about the death of distance, physical proximity is still a major factor in social tie formation and maintenance in virtual social networks. Yet, it is unclear, what are the characteristics of the distance dependence in online social networks. In order to explore this issue the complete network of the former major Hungarian online social network is analyzed. We find that the distance dependence is weaker for the online social network ties than what was found earlier for phone communication networks. For a further analysis we introduced a coarser granularity: We identified the settlements with the nodes of a network and assigned two kinds of weights to the links between them. When the weights are proportional to the number of contacts we observed weakly formed, but spatially based modules resembling to the borders of macro-regions, the highest level of regional administration in the country. If the weights are defined relative to an uncorrelated null model, the next level of administrative regions, counties are reflected.
User activity fluctuations reflect the performance of online society. We investigate the statistical properties of 1-min user activity time series of simultaneously online users inhabited in 95 independent virtual worlds. The number of online users exhibits clear intraday and weekly patterns due to humans circadian rhythms and week cycles. Statistical analysis shows that the distribution of absolute activity fluctuations has a power-law tail for 44 virtual worlds with an average tail exponent close to 2.15. The partition function approach unveils that the absolute activity fluctuations possess multifractal features for all the 95 virtual worlds. For the sample of 44 virtual worlds with power-law tailed distributions of the absolute activity fluctuations, the width of singularity $Deltaalpha$ is negatively correlated with the maximum activity ($p$-value=0.070) and the time to the maximum activity ($p$-value=0.010). The negative correlations are not observed for neither the other 51 virtual worlds nor the whole sample of the 95 virtual worlds. In addition, numerical experiments indicate that both temporal structure and large fluctuations have influence on the multifractal spectrum. We also find that the temporal structure has stronger impact on the singularity width than large fluctuations.
Information spreading in online social communities has attracted tremendous attention due to its utmost practical values in applications. Despite that several individual-level diffusion data have been investigated, we still lack the detailed understanding of the spreading pattern of information. Here, by comparing information flows and social links in a blog community, we find that the diffusion processes are induced by three different spreading mechanisms: social spreading, self-promotion and broadcast. Although numerous previous studies have employed epidemic spreading models to simulate information diffusion, we observe that such models fail to reproduce the realistic diffusion pattern. In respect to users behaviors, strikingly, we find that most users would stick to one specific diffusion mechanism. Moreover, our observations indicate that the social spreading is not only crucial for the structure of diffusion trees, but also capable of inducing more subsequent individuals to acquire the information. Our findings suggest new directions for modeling of information diffusion in social systems and could inform design of efficient propagation strategies based on users behaviors.