Dynamics of information access on the web

While current studies on complex networks focus on systems that change relatively slowly in time, the structure of the most visited regions of the web is altered at the time scale from hours to days. Here we investigate the dynamics of visitation of a major news portal, representing the prototype for such a rapidly evolving network. The nodes of the network can be classified into stable nodes, which form the time-independent skeleton of the portal, and news documents. The visitations of the two node classes are markedly different, the skeleton acquiring visits at a constant rate, while a news document’s visitation peaks after a few hours. We find that the visitation pattern of a news document decays as a power law, in contrast with the exponential prediction provided by simple models of site visitation. This is rooted in the inhomogeneous nature of the browsing pattern characterizing individual users: the time interval between consecutive visits by the same user to the site follows a power-law distribution, in contrast to the exponential expected for Poisson processes. We show that the exponent characterizing the individual user’s browsing patterns determines the power-law decay in a document’s visitation. Finally, our results document the fleeting quality of news and events: while fifteen minutes of fame is still an exaggeration in the online media, we find that access to most news items significantly decays after $36\text{hours}$ of posting.

Figure 1

The cumulative number of visits to a typical skeleton document (a) and a news document (b). The difference between the two visitation patterns allows us to distinguish between news documents and the stable documents belonging to the skeleton.

Figure 2

The skeleton of the studied web portal has 933 nodes. The area of the circle assigned to each node in the figure is proportional to the logarithm of the total number of visits to the corresponding web document. The widths of the links are proportional to the logarithm of the total number of times the hyperlink was used by the surfers on the portal. The central largest node corresponds to the main page (www.origo.hu/index.html) directly connected to several other highly visited sites.

Figure 3

(Color online) (a) The visitation pattern of news documents on a web portal. The data represent an average over 3908 news documents, the release time of each being shifted to day one, keeping the release hour unchanged. The first peak indicates that most visits take place on the release day, rapidly decaying afterward. (b) The same as (a), but to reduce the daily fluctuations we define the time unit as one web page request on the portal. (c) Logarithmic binned decay of visitation of (b) shown in a log-log plot, indicating that the visitation follows $n\left(t\right)\sim {(t+t_0)}^{-\beta }$, with $t_0=12$ and $\beta =0.3\pm 0.1$ shown as a continuous line on both (b) and (c).

Figure 4

(a) The distribution of time intervals between two consecutive visits of users. The cutoff for high $\tau$ $(\tau \approx {10}^6)$ captures finite-size effects, as time delays over a week are undercounted in the month-long data set. The continuous line has slope $\alpha =1.2$. (b) The half-time distribution for individual news items, following a power law with exponent $-1.5\pm 0.1$.

Figure 5

The browsing pattern of four users, every vertical line representing the time of a visit to the main page. The time a news document was released on the main page is shown at $t_0$. The thick vertical bars represent the first time the users visit the main page after the news document was released, i.e., the time they could first visit and read the article.

Figure 6

(a) The distribution of the exponents $a$ for individual users. (b) The numerical results for the visitation decay of a news item [Eq. (7)]. The continuous line represents a slope of 0.14.

Figure 7

We numerically generated browsing patterns for 10 000 users, the distribution of the time intervals between two consecutive visits by the same user following a power law with exponent $\alpha =1.5$. We assume that users visiting the main page will read a given news item with probability $p$. The number of visits per unit time decays as a power law with exponent $\beta =0.5$, for four different values of $p$ (circles for $p=1$, squares for $p=0.7$, diamonds for $p=0.5$, and triangles for $p=0.3$). The empty circles represent the visitation of a news item if the users follow a Poisson browsing pattern. We keep the average time between two consecutive visit of each user the same as the one observed in the real data. As the figure indicates, the Poisson browsing pattern cannot reproduce the real visitation decay of a document, predicting a much faster (exponential) decay.

Figure 8

The distribution of the total number of visits different news documents receive during a month. The tail of the distribution follows a power law with exponent 1.5.