Nonconsensus opinion model on directed networks

Li, Qian; Havlin, Shlomo; Stanley, H. Eugene; Wang, Huijuan

doi:10.1103/physreve.90.052811

Cited by 15 publications

(5 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is known that in many, if not perhaps most, complex systems the interactions between elements are not necessarily symmetric, so they are best described by directed networks (in which edges can be represented with arrows rather than lines). Yet while some authors have studied this characteristic and certain of its effects explicitly [3][4][5][6][7], it is far more common to treat directionality as an afterthought, as though direction were just a random binary number associated with each edge.…”

Section: The Importance Of Being Directedmentioning

confidence: 99%

Digraphs are different: why directionality matters in complex systems

Johnson

2020

J. Phys. Complex.

View full text Add to dashboard Cite

Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect stability, percolation and other dynamical features. I show here that these topological properties have a common origin, in that the edges of directed networks can be aligned-or not-with a global direction. And I illustrate how this can lead to rich and unexpected dynamical behaviour even in the simplest of models.

show abstract

Section: The Importance Of Being Directedmentioning

confidence: 99%

Digraphs are different: why directionality matters in complex systems

Johnson

2020

J. Phys. Complex.

View full text Add to dashboard Cite

show abstract

“…Third, select randomly a fraction 1−ρ of the nodes and shuffle randomly their negative degrees. After the shuffling, the generated degree sequences for the two layers are correlated with linear correlation coefficient ρ [37,38]. Given the negative degree of each node, construct the negative network layer according to the configuration model [39].…”

Section: Signed Network Modelsmentioning

confidence: 99%

Self-avoiding pruning random walk on signed network

Wang

Jiao

et al. 2019

New J. Phys.

Self Cite

View full text Add to dashboard Cite

A signed network represents how a set of nodes are connected by two logically contradictory types of links: positive and negative links. In a signed products network, two products can be complementary (purchased together) or substitutable (purchased instead of each other). Such contradictory types of links may play dramatically different roles in the spreading process of information, opinion, behaviour etc. In this work, we propose a self-avoiding pruning (SAP) random walk on a signed network to model e.g. a user's purchase activity on a signed products network. A SAP walk starts at a random node. At each step, the walker moves to a positive neighbour that is randomly selected, the previously visited node is removed and each of its negative neighbours are removed independently with a pruning probability r. We explored both analytically and numerically how signed network topological features influence the key performance of a SAP walk: the evolution of the pruned network resulted from the node removals, the length of a SAP walk and the visiting probability of each node. These findings in signed network models are further verified in two real-world signed networks. Our findings may inspire the design of recommender systems regarding how recommendations and competitions may influence consumers' purchases and products' popularity.products where two products are connected if when a user is purchasing one product the other product is recommended 3 by the online retail platform like Amazon [24][25][26]. However, these models have not considered the substitute relations between products and the fact that once a product has been purchased, its substitutable products will be unlikely to be purchased afterwards. Hence, we propose in this work a self-avoiding pruning (SAP) walk on a signed network to model, e.g. a user's purchase behaviour on a signed network of products. As shown in figure 1, a SAP walk starts at a random node in a signed network at t=0. At each step, the walker moves from its current location node i to a positive neighbour 4 j that is randomly selected, its previous location, i.e. node i is removed from the signed network 5 and each of node iʼs negative neighbours is removed independently with probability r. The walker repeats such steps until there is no new location to move to. Since each node pair can be connected by either a positive or negative link, but not both, the walker could equivalently, at each step, remove each negative neighbour of its current visiting node i independently with probability r, then move to a random positive neighbour j and afterwards remove the previously visited node i.In the context of a signed product network, a SAP walk may model the purchase trajectory of a user on the network of products: initially, the user purchases a random product and afterwards buys a random complementary product of his/her previous purchase; however, the user will not buy the same product repetitively and unlikely buy the substitutable products of what he/she has bought. If the negative layer is...

show abstract

“…Stochastic models, such as cellular automata [26], Threshold models [27][28][29], Susceptible Infected Recovered (SIR) [17,[30][31][32], and Linear Influence [33] have been studied to understand how the dynamics of information diffusion such as the spreading rate and the social network topology could influence a key feature of the diffusion process such as the popularity. However, we still insufficiently understand to whether such first order models with few parameters could quantitatively reproduce several key features of real-world information diffusion.…”

Section: Introductionmentioning

confidence: 99%

Modelling of information diffusion on social networks with applications to WeChat

Liu

Qü

Chen

et al. 2018

Physica A: Statistical Mechanics and its Applications

Self Cite

View full text Add to dashboard Cite

Traces of user activities recorded in online social networks such as the creation, viewing and forwarding/sharing of information over time open new possibilities to quantitatively and systematically understand the information diffusion process on social networks. From an online social network like WeChat, we could collect a large number of information cascade trees, each of which tells the spreading trajectory of a message/information such as which user creates the information and which users view or forward the information shared by which neighbours. In this work, we propose two heterogeneous non-linear models, one for the topologies of the information cascade trees and the other for the stochastic process of information diffusion on a social network. Both models are validated by the WeChat data in reproducing and explaining key features of cascade trees.Specifically, we firstly apply the Random Recursive Tree (RRT) to model the cascade tree topologies, capturing key features, i.e. the average path length and degree variance of a cascade tree in relation to the number of nodes (size) of the tree. The RRT model with a single parameter θ describes the growth mechanism of a tree, where a node in the existing tree has a probability d θ i of being connected to a newly added node that depends on the degree d i of the existing node. The identified parameter θ quantifies the relative depth or broadness of the cascade trees, indicating that information propagates via a star-like broadcasting or viral-like hop by hop spreading. The RRT model explains the appearance of hubs, thus a possibly smaller average path length as the cascade size increases, as observed in WeChat. We further propose the stochastic Susceptible View Forward Removed (SVFR) model to depict the dynamic user behaviors including creating, viewing, forwarding and ignoring a message on a given social network. Beside the average path length and degree variance of the cascade trees in relation to their sizes, the SVFR model could further explain the power-law cascade size distribution in WeChat and unravel that a user with a large number of friends may actually have a smaller probability to read a message (s)he receives due to limited attention.

show abstract

Nonconsensus opinion model on directed networks

Cited by 15 publications

References 51 publications

Digraphs are different: why directionality matters in complex systems

Digraphs are different: why directionality matters in complex systems

Self-avoiding pruning random walk on signed network

Modelling of information diffusion on social networks with applications to WeChat

Contact Info

Product

Resources

About