Role of social environment and social clustering in spread of opinions in coevolving networks

Abstract

Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the coevolving network voter model of opinion formation studied by Holme and Newman [Phys. Rev. E 74, 056108 (2006)]. First, we replace the rewiring probability parameter by a distribution of probability of accepting or rejecting opinions between individuals, accounting for heterogeneity and asymmetric influences in relationships between individuals. Second, we modify the rewiring step by a path-length-based preference for rewiring that reinforces local clustering. We have investigated the influences of these modifications on the outcomes of simulations of this model. We found that varying the shape of the distribution of probability of accepting or rejecting opinions can lead to the emergence of two qualitatively distinct final states, one having several isolated connected components each in internal consensus, allowing for the existence of diverse opinions, and the other having a single dominant connected component with each node within that dominant component having the same opinion. Furthermore, more importantly, we found that the initial clustering in the network can also induce similar transitions. Our investigation also indicates that these transitions are governed by a weak and complex dependence on system size. We found that the networks in the final states of the model have rich structural properties including the small world property for some parameter regimes. As the study of networks is applied to an ever broadening variety of phenomena, it is important to study the properties of networks, dynamical processes coupled across networks, and the interplay between the two where the coupled dynamics affect the network topology. A minimal mathematical model that has been used to model the social phenomena of collective opinion formation is the coevolving voter model. 1,[16][17][18][19][20][21][22][23][24][25][26] We introduce two additional attributes to the multi-opinion coevolving voter model, in order to describe processes and networks that are closer to real-world situations within a still relatively simple model. Our model includes a "social environment," modeling the inherent heterogeneity and asymmetry in relationships within a social group. We also include a path-length-based preference for rewiring that reinforces social clustering. Our inclusion of this second attribute has been influenced by the fact that clustering is a ubiquitous feature of networks and has not been incorporated as a dynamic entity in most coevolving voter models. We explore the consequences of these two additional attributes within the coevolving voter model, comparing and contrasting the behaviors of this only slightly more complicated model with those of the minimal coevolving voter model. Our results highlight the important role of clustering, with possible consequences for future applications of coevolving voter models.

Separating temporal and topological effects in walk-based network centrality

“…Degree heterogeneity is one such topological feature which is not nullified by shuffling. On the other hand, features like community structure, assortativity and clustering are likely to play a significant role in determining the communicability in most applications of this work [39][40][41]. Similarly, the non-shuffled data is likely to exhibit certain temporal features.…”

Transitivity reinforcement in the coevolving voter model

“…In this model, connected nodes with discordant opinions are resolved by one neighbor in the pair either changing its opinion or dropping the connection (in favor of a newly rewired connection to another node in the network). This model reproduces several complex features observed in collective opinion formation and has led to a variety of computational and analytical results on different aspects of the model [1,2,10,15,16,18]. However, all previous variants of this model (including those studied by the present authors) have ignored one of the most fundamental features of networks, namely the higher propensity for a connection between two nodes that are both already connected to a third node, closing the triangle between them [5].…”

“…The study of dynamics on networks has led to a number of successes identifying how the structure of the underlying network impacts the dynamics occurring on the network [1][2][3] and whether dynamics taking place on the network also promotes organizing features of the network structure itself [4][5][6]. Within this larger research theme, significant attention has been given to exploring the role of network structures on the spread of contagions and opinions [1,7,8,10], including efforts to understand and quantify features in the spread of contagions due to different local and global structural properties [11,12]. The study of opinions spreading in social networks has gained additional interest due to the rise of social media and its role in mobilizing and framing public opinion [13], including elections and advertising campaigns [14].…”

Relationship between network clustering in a therapeutic community and reincarceration following discharge

“…If A is friends with both B and C, who are friends with each other, the triad is closed. It is quite common for such triads to be closed; as the saying goes, the friend of my friend is also a friend (Malik & Mucha, 2013;Malik, Shi, Lee & Mucha, 2016).…”