Social media, regarded as two-layer networks consisting of users and items, turn out to be the most important channels for access to massive information in the era of Web 2.0. The dynamics of human activity and item popularity is a crucial issue in s
ocial media networks. In this paper, by analyzing the growth of user activity and item popularity in four empirical social media networks, i.e., Amazon, Flickr, Delicious and Wikipedia, it is found that cross links between users and items are more likely to be created by active users and to be acquired by popular items, where user activity and item popularity are measured by the number of cross links associated with users and items. This indicates that users generally trace popular items, overall. However, it is found that the inactive users more severely trace popular items than the active users. Inspired by empirical analysis, we propose an evolving model for such networks, in which the evolution is driven only by two-step random walk. Numerical experiments verified that the model can qualitatively reproduce the distributions of user activity and item popularity observed in empirical networks. These results might shed light on the understandings of micro dynamics of activity and popularity in social media networks.
Inspired by the analysis of several empirical online social networks, we propose a simple reaction-diffusion-like coevolving model, in which individuals are activated to create links based on their states, influenced by local dynamics and their own i
ntention. It is shown that the model can reproduce the remarkable properties observed in empirical online social networks; in particular, the assortative coefficients are neutral or negative, and the power law exponents are smaller than 2. Moreover, we demonstrate that, under appropriate conditions, the model network naturally makes transition(s) from assortative to disassortative, and from sparse to dense in their characteristics. The model is useful in understanding the formation and evolution of online social networks.
The dynamical origin of complex networks, i.e., the underlying principles governing network evolution, is a crucial issue in network study. In this paper, by carrying out analysis to the temporal data of Flickr and Epinions--two typical social media
networks, we found that the dynamical pattern in neighborhood, especially the formation of triadic links, plays a dominant role in the evolution of networks. We thus proposed a coevolving dynamical model for such networks, in which the evolution is only driven by the local dynamics--the preferential triadic closure. Numerical experiments verified that the model can reproduce global properties which are qualitatively consistent with the empirical observations.
In order to investigate the role of the weight in weighted networks, the collective behavior of the Ising system on weighted regular networks is studied by numerical simulation. In our model, the coupling strength between spins is inversely proportio
nal to the corresponding weighted shortest distance. Disordering link weights can effectively affect the process of phase transition even though the underlying binary topological structure remains unchanged. Specifically, based on regular networks with homogeneous weights initially, randomly disordering link weights will change the critical temperature of phase transition. The results suggest that the redistribution of link weights may provide an additional approach to optimize the dynamical behaviors of the system.
Do scientists follow hot topics in their scientific investigations? In this paper, by performing analysis to papers published in the American Physical Society (APS) Physical Review journals, it is found that papers are more likely to be attracted by
hot fields, where the hotness of a field is measured by the number of papers belonging to the field. This indicates that scientists generally do follow hot topics. However, there are qualitative differences among scientists from various countries, among research works regarding different number of authors, different number of affiliations and different number of references. These observations could be valuable for policy makers when deciding research funding and also for individual researchers when searching for scientific projects.
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the observations of r
eal social networks, we introduced a link-creating/deleting strategy according to the local dynamics in the model. Thus the coevolution of dynamics and topology naturally determines the network properties. It is found that for a small coupling strength, the networked system cannot reach any synchronization and the network topology is homogeneous. Interestingly, when the coupling strength is large enough, the networked system spontaneously forms communities with different dynamical states. Meanwhile, the network topology becomes heterogeneous with modular structures. It is further shown that in a certain parameter regime, both the degree and the community size in the formed network follow a power-law distribution, and the networks are found to be assortative. These results are consistent with the characteristics of many empirical networks, and are helpful to understand the mechanism of formation of modularity in complex networks.
By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes, so this kin
d of networks is named as the weight-degree correlated (WDC) network. In scheme-II, the link weights are randomly assigned to each link regardless of the node degrees, so this kind of networks is named as the weight-degree uncorrelated (WDU) network. Interestingly, it is found that by increasing a parameter that governs the weight distribution, the onset of synchronization in WDC network is monotonically enhanced, while in WDU network there is a reverse in the synchronization performance. We investigate this phenomenon from the viewpoint of gradient network, and explain the contrary roles of coupling gradient on network synchronization: gradient promotes synchronization in WDC network, while deteriorates synchronization in WDU network. The findings highlight the fact that, besides the link weight, the correlation between the weight and node degree is also important to the network dynamics.
In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously differentiate into t
wo dynamical groups after a long time evolution. Within each group, the oscillators have similar phases, while oscillators in different groups have approximately opposite phases. The network gradually converts from the initial random structure with a uniform distribution of connection strengths into a modular structure which is characterized by strong intra connections and weak inter connections. Furthermore, the connection strengths follow a power law distribution, which is a natural consequence of the coevolution of the network and the dynamics. Interestingly, it is found that if the inter connections are weaker than a certain threshold, the two dynamical groups will almost decouple and evolve independently. These results are helpful in further understanding the empirical observations in many social and biological networks.
Global degree/strength based preferential attachment is widely used as an evolution mechanism of networks. But it is hard to believe that any individual can get global information and shape the network architecture based on it. In this paper, it is f
ound that the global preferential attachment emerges from the local interaction models, including distance-dependent preferential attachment (DDPA) evolving model of weighted networks(M. Li et al, New Journal of Physics 8 (2006) 72), acquaintance network model(J. Davidsen et al, Phys. Rev. Lett. 88 (2002) 128701) and connecting nearest-neighbor(CNN) model(A. Vazquez, Phys. Rev. E 67 (2003) 056104). For DDPA model and CNN model, the attachment rate depends linearly on the degree or strength, while for acquaintance network model, the dependence follows a sublinear power law. It implies that for the evolution of social networks, local contact could be more fundamental than the presumed global preferential attachment. This is onsistent with the result observed in the evolution of empirical email networks.
Based on signaling process on complex networks, a method for identification community structure is proposed. For a network with $n$ nodes, every node is assumed to be a system which can send, receive, and record signals. Each node is taken as the ini
tial signal source once to inspire the whole network by exciting its neighbors and then the source node is endowed a $n$d vector which recording the effects of signaling process. So by this process, the topological relationship of nodes on networks could be transferred into the geometrical structure of vectors in $n$d Euclidian space. Then the best partition of groups is determined by $F$-statistic and the final community structure is given by Fuzzy $C$-means clustering method (FCM). This method can detect community structure both in unweighted and weighted networks without any extra parameters. It has been applied to ad hoc networks and some real networks including Zachary Karate Club network and football team network. The results are compared with that of other approaches and the evidence indicates that the algorithm based on signaling process is effective.
