Abstract
Statistical properties of the static networks have been extensively studied. However, online social networks are evolving dynamically, understanding the evolving characteristics of the core is one of major concerns in online social networks. In this paper, we empirically investigate the evolving characteristics of the Facebook core. Firstly, we separate the Facebook-link(FL) and Facebook-wall(FW) datasets into 28 snapshots in terms of timestamps. By employing the k-core decomposition method to identify the core of each snapshot, we find that the core sizes of the FL and FW networks approximately contain about 672 and 373 nodes regardless of the exponential growth of the network sizes. Secondly, we analyze evolving topological properties of the core, including the k-core value, assortative coefficient, clustering coefficient and the average shortest path length. Empirical results show that nodes in the core are getting more interconnected in the evolving process. Thirdly, we investigate the life span of nodes belonging to the core. More than 50% nodes stay in the core for more than one year, and 19% nodes always stay in the core from the first snapshot. Finally, we analyze the connections between the core and the whole network, and find that nodes belonging to the core prefer to connect nodes with high k-core values, rather than the high degrees ones. This work could provide new insights into the online social network analysis.
Highlights
Online social networks are organized around participating users who create interactions with whom they associate [1,2,3]
We focus on investigating the set of most influential nodes in online social networks, which is defined as the nodes with the highest kcore value [12]
We suggest that when the Facebook quickly becomes popular and attracts large amounts of users, the most influential and active users will inhabit in the Facebook core for long time
Summary
Online social networks are organized around participating users who create interactions with whom they associate [1,2,3]. An in-depth investigation of the evolving network core is very important for deeply understanding the evolving characteristics of online social networks [6,7], where the core could be identified by the k-core decomposition method [8]. Miorandi et al [13], Ren et al [14] extended the k-core decomposition method to identify the node spreading influence in networks, and Garas et al [15] presented a generalized method for calculating the k-core structure of weighted networks. These works have similar conclusions that nodes belonging to the core are the most influential spreaders. We empirically analyze the evolution characteristics of the Facebook’s core, and the statistical results indicate that (1) The core sizes of the Facebook-link(FL) and Facebook-wall(FW) networks are approximately stable around 672 nodes and 373 nodes respectively. (2) Nodes belonging to the core get more interconnected, and their k-core values increase correspondingly. (3) The life span analysis of the nodes belonging to the core reveals that more than 50% nodes stay in the core for more than one year, and 19% nodes always stay in the core from the first snapshot. (4) The nodes in the core prefer to connect to high k-core nodes, regardless of the high degree ones
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