(1) \emph{lead}: all links in the first section of the article excluding infobox, (2) \emph{body}: all other links in the main text, (3) \emph{left-body}: links in the body that are displayed in the 10\% most left part of the screen, (4) \emph{right-body}: links in the remaining right part of the body, (5) \emph{infobox}: all links in the infobox, (6) \emph{navbox}: all links in a table in the last section of the article placed by editors for facilitating navigation. As links can occur multiple times on an article, we derived the visual position of a link based on its first occurrence on the screen. This goes hand-in-hand with our empirical results elaborated in Section 4.2. A more detailed discussion about this facet of our data is provided in Section 7.

\section{Focus of Attention}

We start our analysis by investigating the focus of attention with respect to link usage in Wikipedia, i.e., we study how strongly user transitions are concentrated on the few most visited links.

\textbf{Distribution of transition counts.} As a first key statistic, we observe that of \textasciitilde340 million links in $D_{wiki}$ only about 13.6 million links (or about 4\% of all links) are regularly used, i.e., are visited at least 10 times within a month. However, even when considering only these 4\% regularly used links, we can observe that users focus heavily on a comparatively small set of links: about 50\% of all transitions stem from only about 600{,}000 links. A frequency plot of the distribution, see Figure~\ref{fig:figure_2}(a), reveals a long-tailed distribution, where most of the links receive very low amounts of transitions.

\textbf{Out-degree distribution.} A similar effect can be observed at the level of individual articles. We compare the out-degree distributions of nodes in $D_{wiki}$ and $D_{trans}$, i.e., we compare the number of available links on articles in $D_{wiki}$ with the number of regularly used links in $D_{trans}$. For a fair comparison, we consider only the out-degrees of nodes that occur in both networks. The results in Figure~\ref{fig:figure_2}(b) reveal clear differences. The out-degree distribution of $D_{wiki}$ reaches a maximum frequency for articles having eleven out-links indicating a decent amount of links to choose from. However, the out-degree distribution of $D_{trans}$ clearly reveals that for most articles, users only visit a few articles regularly with the maximum frequency of only a single link. Formal comparison of both distributions with respect to (truncated) power-law, exponential, and log-normal distributions by their goodness of fit reveals that for $D_{trans}$ the out-degree distribution resembles a truncated power-law most closely, while for $D_{wiki}$ a log-normal distribution is preferred.

\textbf{Gini coefficient of transition counts.} The previous analyses have suggested a discrepancy between the link network $D_{wiki}$ and actually transitioned links in $D_{trans}$. The Gini coefficient is a measure of statistical dispersion allowing us to quantify the inequality of link popularity within articles. We calculate the Gini coefficient for each article based on a vector containing the transition counts for all links (including zeros) in this article from $D_{trans}$. A Gini coefficient of 0 indicates complete equality, while a result of 1 would mean that only a single link gets the whole attention. We visualize the histogram of all coefficients for each article in Figure~\ref{fig:figure_2}(c); results indicate that there is a clear inequality of link popularity within articles, i.e., attention focuses on just a few links.

\textbf{Summary.} In this section, we have presented empirical evidence that on Wikipedia user attention focuses on a small set of links while navigating. This hints towards a clear preference towards a few links and demonstrates the importance of finding indicators of link success, on which we focus in the remainder of this paper.

\section{What Makes a Link Successful?}

Motivated by the discrepancy between link presence and link usage, we now study link success. That is, as illustrated in Figure~\ref{fig:figure_1}, given a Wikipedia article, we aim at identifying effects of link features (network features, semantic features, or visual features) on counts of transitions to the respective target article. This allows us to answer questions such as: ``Are links leading to peripheral articles more popular and thus, more successful?'' We propose a methodology in Section 4.1 and discuss results in Section 4.2.

\subsection{Methodology}

For studying effects of link features on the success of links, we employ descriptive statistics and \emph{hurdle mixed-effects regression models}; we outline both approaches next.

\textbf{Descriptive analysis.} We start our analysis with a descriptive overview on the effects of our features on transition counts. For an intuitive picture, we investigate boolean expressions on our features and determine for each feature the number of links, the number of transitions, and the average number of transitions per link. We focus on easy-to-interpret expressions: for network features, we compare the centrality of the target node with the centrality of the source node. For semantic similarity features, we compare the similarity between source and target article of the link with the median of the respective values for all links within the same source article. Finally, for the visual features, we divide the screen position in three areas for each dimension, that is the left, the middle, and the right third of the screen, and links in the top-half, the bottom-half and links that are only visible after vertical scrolling (assuming a resolution of 1920 $\times$ 1080) respectively. Furthermore, we use the position of the link in a specific part of the article such as the lead or the infobox.

\textbf{Mixed-effects hurdle model.} Additionally, we aim at statistically modeling the effects of all link features on link success given a certain start node. Our setting (cf. Figure~\ref{fig:figure_1}) implies that individual links represent data points with the transition counts being the outcome to predict, and the respective link features the effects at interest. Yet, links in the dataset are not independent of each other, but rather nested within Wikipedia articles. Heterogeneous effects might be present as e.g., apart from generally different amounts of total transitions, the article of ``Manchester'' might pose different navigational behavior than the article of ``USA''. Pooling all links into a single dataset for ordinary regression can lead to biased results; consequently we resort to \emph{mixed-effects models} (also known as multilevel models or hierarchical models), allowing us to account for the nested structure---specifically the resulting random variations---between links (level 1) and Wikipedia pages (level 2). We define our mixed-effects model following \cite{18}; for a broader introduction we point to \cite{33}:

\begin{equation}
Y_{i,j} = \gamma_{0,0} + \gamma_{1,0} X_{1,i,j} + u_{0,j} + u_{1,j} X_{1,i,j} + e_{i,j}
\label{eq:1}
\end{equation}

Here, $Y_{i,j}$ refers to the transition count of a link $i$ (level 1) on a Wikipedia page $j$ (level 2); $\gamma_{0,0}$ refers to the overall intercept and $\gamma_{1,0}$ to the overall regression coefficient for the level 1 predictor $X_{1,i,j}$, e.g., the degree of the target node.