Evolution of disconnected components in social networks: Patterns and a generative model

Abstract

The majority of previous studies have focused on the analyses of an entire graph (network) or the giant connected component in a graph. Here we study the disconnected components (non-giant connected components) in real social networks, and reporting some interesting discoveries on how these disconnected components evolve over time. We study six diverse, real networks (citation networks, online social networks, academic collaboration networks, and others), and make the following major contributions: (a) we make empirical observations of the longevity distribution of disconnected components, and find that the curve of the distribution demonstrates a decaying trend; (b) we find that the distributions of final size of disconnected components that merge with one another or get absorbed by the giant connected component both follow power laws; (c) we find that the majority of mergings are between disconnected components and the giant connected component. The mergings that happen among disconnected components are small in scale (involve only a few components). The longevity distributions of the disconnected components in those mergings are similar, where the shortest-lived disconnected components are the most in number; and (d) we propose an empirical generative model that can produce the networks with our observed patterns.

Structural properties and generative model of non-giant connected components in social networks

“…From Figures 3(b) and (c), we can discover that the portion of merging among DCs is relatively small and the majority of DCs are absorbed by GCC. These observations are consistent with the discoveries in [6].…”

“…The network generated by our proposed iFriends model should obey structural properties observed in Section 3 as well as properties observed in previous work, such as the properties observed in [6].…”

“…But in real networks, there often exist many disconnected components (DCs), which are relatively independent, small components that do not connect with any other components. In earlier work, some interesting properties of DCs have been discovered, such as the star-shaped "middle regions" [4], the "gelling point" of the network diameter [5], and the final size power law [6]. In this paper, we turn our attention to the analyses of these DCs.…”

Effective Techniques for Message Reduction and Load Balancing in Distributed Graph Computation

“…We consider fundamental problems such as (1)computing connected components (or bi-connected components), which is a common preprocessing step for social network analysis [14,15]; (2)computing minimum spanning tree (or forest), which is useful in mining social relationships [15]; and (3)computing PageRank, which is widely used in ranking web pages [16,9] and spam detection [7].…”