Influence of Temporal Aspects and Age-Correlations on the Process of Opinion Formation Based on Polish Contact Survey

Abstract

On the basis of the experimental data concerning interactions between humans the process of Ising-based model of opinion formation in a social network was investigated. In the paper the data concerning human social activity, i.e. frequency and duration time of interpersonal interactions as well as age correlations - homophily are presented in comparison to base line homogeneous, static and uniform mixing. Recent research suggests that real (temporal and assortative) patterns can both speed up or slow down processes (like epidemic spread) on the networks. Also in our study, a real structure of contacts affects processes of opinion formation in various non-intuitive ways. The real patterns (correlation and dynamics) reduce ‘freezing by heating’ effect for small social temperature values. Moreover, our research shows that the cross interactions between contact frequency and its duration impose the significant increase in critical temperature.

A Appendix: Network Model

In all scenarios degree distribution is fixed (to empirical one). However, by introducing temporal aspects or homophily other non-fixed structural properties as community structure may change.

The local clustering structure (with communities structure) change with modification of base static network (Fig. 5a). The most important difference cause age-correlations, which induce huge communities instead of many medium size communities (Fig. 6a). Thus, homophily decreases on average local clustering coefficient, so age-correlated network is less tided. Moreover, seniors and children (Fig. 5b) are places on periphery (far away form centers of the network), because of their small degree (Fig. 2b) as well as clustering (Fig. 5b).

The dynamic rewiring (corresponds to around 25% of the network) does not change clustering structure very much (Fig. 5a) because most of temporal links are sampled from local neighborhood. Links show very long memory. Totally random links (which correspond to empirical ‘random’ contacts sampled from entire population) are in minority, because ‘average of mass’ is situated in loyal - repeatable links (corresponding to empirical ‘rare’ contacts sampled from bounded population). We define Loyalty as a measure of repeatability of the link. Loyalty of a single link occurrence takes the nominal value ‘unique’.

Fig. 5.

The local clustering coefficient for given cohort of nodes: (a) in function of degree with various scenarios; (b) in function of age for the age-correlated network. Note that non-correlated and static networks are equivalent.

Fig. 6.

(a) The Rank-size distribution of communities based on Louvain detection algorithm (with age-age correlations - solid line and without age-age correlations - dashed line). (b) Descriptive statistics for the number of loyal neighbors (first and second choice) of each node in the dynamic part of the network.

The range of variability in neighbors can be describes in terms of most frequent connections. Totally random re-wiring is not likely to form loyal connections (maximum Loyalty $\sim$ 4%). Thus most of temporal neighbors are limited to relatively small population. There are around 4 first choice neighbors (the most loyal neighbors appearing more than 40% of time) and around 8 second choice neighbors (neighbors appearing more less than 40% but more than 4% of time) (Fig. 6b). These second choice neighbors could be called ‘weak’ ties [11] between the communities that could have a different opinion.