For example, Twitter is a directed network of follow-following relationship, while QQ in our research is an un-directed network with reciprocal relationships. There may be discrepancies in behaviors pattern aroused by the types of relationship, such as transferring information or causing behaviors. We use SCos to measure mobility similarity owing to its simplicity, universality and high efficiency although only spatial information is considered in it.
However, in recent researches, many alternative metrics have been raised to describe mobility similarity more accurately and reasonably with temporal, personal or global factors 28 , 42 , In order to verify whether the current results are robust to other similarity metrics, we choose Co-location rate CoL 28 which incorporates temporal information to measure mobility similarity.
CoL calculates the probability of two individuals going to the same destination at the same time, i. Similar phenomenon can be observed from the experiment results based on CoL that befriending, having common friends and diversity of common friends all have positive influence on mobility similarity, indicating the robustness of our conclusion see Supporting Information.
Mobile Social Networking - An Innovative Approach | Alvin Chin | Springer
Besides, there are many other metrics to measure social proximity in a network. For example, the concept edge-connectivity between two nodes s and t in a graph which is counted as the minimum number of links must be removed to destroy all paths from s to t , is always used to measure the reachability between two nodes 44 , Intuitively, the more independent pathways between two nodes, the closer their relationship is.
We calculate the edge-connectivity of each pair, and then report the results in Supporting Information. A similar pattern can be observed that edge-connectivity has no positive impact on mobility similarity, just like CN. Consequently, the results again support our conclusion that neither the number of common friends nor the number of pathways between two individuals plays a positive role in increasing the mobility similarity between them. The preference or personality also affects individual mobility pattern and similarity. Song et al. Later in ref.
We apply their method to our dataset and observe a consistent phenomenon that the mobility similarity between the same class of individuals group explorer-explorer and returner-returner is obviously higher than that of different class group explorer-returner. More details can be seen in Supporting Information. Our analysis provides a statistical view of the coupling between human online social proximity and offline mobility similarity, and inspires deep understanding to the intrinsic of topological structure when predicting offline behaviors.
Generally, the social network and check-in records correspond to real physical layer and virtual social layer in nature world and human society. Therefore, the LBSN data we used provides a good medium to couple physical space and social space. Technically, our results could offer new insight and evidence in the fields of location prediction and friend recommendation For example, mining human mobility pattern and leveraging social network information for next location prediction of a certain individual is always a big challenge.
Our study opens a door to a series of open questions.
Mobile Social Networking: An Innovative Approach
It is challenging and valuable to explain the fact that mobility similarity depends on the existence, but not the size, of online common neighbors. It remains unknown whether the effect of common neighbors could be generalized to more scenarios, before adequate empirical analysis is done on different types of social networks. It is also valuable to explore effect of common neighbors built with different types of edges, e. Our data is authorized by a Chinese online service provider Tencent, whose instant message product QQ and mobile check-in service provides the social network information and temporal-spatial mobility records respectively.
QQ Users make friends and chat with them online as well as travel around offline in their daily life. Accordingly, on one hand, the social proximity between individuals can be depicted by the network structure. On the other hand, the trajectory sequence of each user and the similarity of mobility pattern between two individuals can be obtained as well. Therefore, this comprehensive dataset includes well coupled human online and offline behaviors.
We were the first to analyze this dataset. Specifically, The users are sampled from a coastal city of China, while their check-in records cover the whole region of Chinese mainland. The dataset contains three parts of information, namely, individual demographic information, social relationship and time-stamped check-in records longitude and latitude with an error no greater than 0. We remove inactive users with less than check-ins for stable statistics, resulting in a dataset of 97, users with , friend links and 28,, check-in records during the second half of year The average degree, average clustering coefficient and assortative coefficient of the social network is 6.
S1 , the degree distribution of social network follows power-law function with exponential cutoff. Only locations and its visit frequency is considered in this measurements, without considering the visiting sequence. These two metrics measure the strength and similarity of social relationship from online and offline aspects. We calculate CN and SCos for all pairs of friends in our dataset, and obtain the distributions of these two metrics see Supporting Information. It can been observed that both distributions derive from normal or approximate normal distribution. The results provide not only a description of heterogeneity of human behavior and society but also a evidence of choosing a appropriate correlation coefficient.
Due to the sparsity of social network the network density in this study is only 0. To reduce statistical error and computational complexity, we randomly select equal-sized pairs of non-friends as friends for the comparative study in the discrepancy of mobility similarity between them Fig.
Mobile Social Networking : An Innovative Approach
Considering that the degree distribution of our social network behaves heavy-tail shape, i. Specifically, we adopt the sampling without replacement method to pick out friends to ensure that every individual appear in the sample only once to avoid the influence from the hub nodes with plenty of links. In the sampling process, once a edge is chosen, the two nodes connected by it will be removed from the sample pool. The obtained samples are used for investigating the mobility similarity of friends with different number of common neighbors.
The sampling is processed as follows. There are nearly 10 thousands nodes and over thousands edges in the social network initially. Finally some isolated nodes without any friend may be left and they are neglected. Thereby an ego-social network 25 , 46 is obtained where every edge represent a pair of individuals whose similarity is measured by CN and SCos.
The sampling process is carried out for times to ensure the randomness. In every sample, we have about 70 thousands nodes and nearly 40 thousands edges. Take 1 out of experiments as an example, 38, edges are obtained, within which 24, pairs of friends have no common neighbors and the remaining have at least one. After sampling, unbiased test is used to ensure that all the samples keep consistent with each other. Specifically, we calculate the mean and std of SCos and plot their distributions, which show a narrowed unimodal shape, illustrating that the samples are unbiased.
Kolmogorov-Smirnov test KS test is a kind of nonparameter test which can be used to verify whether two empirical samples are drawn from the same distribution. The KS statistic quantifies a distance between the empirical distribution functions of two samples. The null distribution of this statistic is calculated under the null hypothesis that the samples are drawn from the same distribution.
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The procedure of KS test can be seen in ref. Besides, the null hypothesis is set as that the distribution samples are independent identically distributed i. If the tested two distributions are not i. However, Fig. S5 demonstrates that all the distributions are not normally distributed, indicating that the two distributions are drawn from the same population. Electronic supplementary material. Supplementary information accompanies this paper at Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
National Center for Biotechnology Information , U. Sci Rep. Published online Sep China Find articles by Chao Fan.
copegus.top/the-analysis-of-covariance-and.php China Find articles by Yiding Liu. China Find articles by Zhihai Rong. China Find articles by Tao Zhou. Author information Article notes Copyright and License information Disclaimer. Junming Huang, Email: moc. Corresponding author. Received Sep 27; Accepted Sep 6.