Structure and evolution of online social relationships: Heterogeneity in unrestricted discussions

With the advancement in the information age, people are using electronic media more frequently for communications, and social relationships are also increasingly resorting to online channels. While extensive studies on traditional social networks have been carried out, little has been done on online social networks. Here we analyze the structure and evolution of online social relationships by examining the temporal records of a bulletin board system (BBS) in a university. The BBS dataset comprises of 1908 boards, in which a total of 7446 students participate. An edge is assigned to each dialogue between two students, and it is defined as the appearance of the name of a student in the from- and to-field in each message. This yields a weighted network between the communicating students with an unambiguous group association of individuals. In contrast to a typical community network, where intracommunities (intercommunities) are strongly (weakly) tied, the BBS network contains hub members who participate in many boards simultaneously but are strongly tied, that is, they have a large degree and betweenness centrality and provide communication channels between communities. On the other hand, intracommunities are rather homogeneously and weakly connected. Such a structure, which has never been empirically characterized in the past, might provide a new perspective on the social opinion formation in this digital era.

Figure 1

(Color online) Schematic network snapshots of the BBS network (a) and traditional social network (b).

Figure 2

Structure of the BBS network. (a) The degree distribution $P_d\left(k\right)$ $(\circ )$ and the strength distribution $P_s\left(s\right)$ $(◇)$ of the entire network. The straight line is a guideline with a slope of $-1$. (b) The degree-strength scaling relation $s\left(k\right)$. The straight line is a guideline with a slope of $1.4$. (c) The clustering function $C\left(k\right)$ $(\circ )$ and its weighted version $(◇)$. The straight lines are guidelines with slopes of $-0.5$ (lower) and $-0.3$ (upper), respectively. (d) The average nearest-neighbor degree function $k_{\mathrm{nn}}\left(k\right)$ and its weighted version $(◇)$. (e) The correlation between the degree and the membership number $B$. The dotted line is a guideline with a slope of $1$. (f) The membership number distribution of the vertices $P_B\left(B\right)$, where $B$ is the number of boards that a student participates in. The straight line is a guideline with a slope of $-1$.

Figure 3

(a) The betweenness centrality (BC) distribution of the BBS network. The dotted line is a guideline with a slope of $-2.2$. (b) The relation between BC $(\ell )$ and degree $\left(k\right)$ of the BBS network. The dotted line is a guideline with a slope of $1.6$.

Figure 4

Structure of the board network. (a) The degree distribution $P_d\left(k\right)$ $(\circ )$ and strength distribution $P_s\left(s\right)$ $(◇)$ of the board network. (b) The degree-strength relation in the board network. The straight line is a guideline with a slope of $1$. (c) The clustering function $C\left(k\right)$ $(\circ )$ and its weighted version $(◇)$. (d) The average nearest-neighbor degree function $k_{nn}\left(k\right)$ $(\circ )$ and its weighted version $(◇)$.

Figure 5

Properties of the board subnetwork. (a) The degree distributions of subnetworks within the five largest boards. Symbols used are $(\circ )$, $(▵)$, $(◇)$, $(◻)$, and $(▿)$ in the decreasing order of board size. The fitted curves with the gamma distribution $k^{a-1}{e}^{-k∕b}∕\left[\Gamma \right(a\left)b^a\right]$ are shown. (b) The degree distributions of subnetworks within the five largest boards with degrees redefined as discussed in the text. (c) The size distribution of the boards $P_M\left(M\right)$. The straight line is a guideline with a slope of $-0.7$. (d) The link density $\Lambda \left(M\right)$ within a board as a function of its size $M$. The straight line is a guideline with a slope of $-0.65$.

Figure 6

Evolution of the BBS network. (a) The temporal evolution of the number of students $N$ (solid), number of links $L$ (dashed), total number of dialogs $W$ (dotted), and the number of boards $G$ (dot-dashed). (b) The same plot as (a) in the double logarithmic scale. (c) The evolution of the degree distribution $P_d\left(k\right)$ of the student network. The degree distribution for each year is shown. The symbols $(\circ )$, $(◇)$, $(▵)$, and $(▿)$ correspond to each year from 2001 to 2004, respectively, and $(◻)$ represents the final configuration. (d) The clustering function $C\left(k\right)$ for each year. The same symbols as those in (c) are used.

Figure 7

Comparison of the degree distributions of a simple model of the BBS network of Newman (dotted) and its modification (solid), with that of the real network (circle).