The hierarchical organization of real-world networks.

w<p>Weighted links.</p>d<p>Directed links.</p><p>*Dual representation with roads as nodes and intersections as edges.</p><p>For each multi-level classification of a network with nodes and links, we report the total number of modules together with the number of modules with more than one percent of all nodes, the per-node average depth , the per-node average size of the lowest-level module , and the compression gain over a two-level clustering . The 12 networks are ordered by the compression gain, which provides information about how hierarchical the organization is.</p

A hierarchical map of science.

<p>We partitioned 7,940 journals connected by 9.2 million citations <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018209#pone.0018209-Rosvall3" target="_blank">[20]</a> into four major disciplines, which we identified as life sciences, physical sciences, ecology and earth sciences, and social sciences. In physical sciences, we followed a second-level split into the areas of mathematics and of physics and chemistry. The size of the modules represents the fraction of time that a random surfer spends following citations in that field, and the arrows indicate flow volume between the fields. For visual simplicity, we exclude fields and arrows with low flow.</p

Hierarchical benchmark test.

<p>Figures A–D show how well the algorithm reveals the three-level organization of the hierarchical benchmark networks with 10,000 nodes and 100,000 links. The nodes share a fraction of their links with nodes in other coarse-level modules and a fraction of their links with nodes in other fine-level modules. Every data point represents the average value of 100 measures.</p

The range of mixing parameters that give a well-defined three-level hierarchical structure for the benchmark networks in the paper.

<p>The networks have nodes, coarse-level module sizes between and nodes, and fine-level module sizes between and nodes. The connected points illustrate the sets of mixing parameters we present in the paper.</p

Distribution of author number over time for the JSTOR corpus.

<p>Multi-authored papers have increased over time while the fraction of single-authored papers have declined. The y-axis is the percentage of papers with the given number of authors. The legend shows “A”, the number of authors on a paper.</p

Even in fields with a gender composition near parity, men (blue bars) and women (pink bars) are unequally distributed in subfields.

<p>Shown here is sociology and its subfields from 1990 to the present. An interactive version of this graph, covering all fields and subfields of the JSTOR network dataset, is available online at <a href="http://www.eigenfactor.org/gender/" target="_blank">http://www.eigenfactor.org/gender/</a>.</p

Gender as a function of authorship order across the entire JSTOR network dataset.

<p>Top panel: 888,060 authorships prior to 1990. Bottom panel: 1,156,354 authorships from 1990 to the present. From 1990 to present, women are no longer severely underrepresented as first author, but they are increasingly underrepresented as last author. Error bars indicate one standard deviation of the binomial distribution. For the graph of author position, the solid line indicates the overall frequency of women in the JSTOR network dataset. For the last-author graph, the point indicates the frequency of women who are last author on papers with at least three authors. The horizontal line in this part of the graph indicates the appropriate comparator: the overall frequency of women in any authorship position on papers with three or more authors.</p

Percentage of women relative to total PhDs and percentage of women in tenure or tenure track positions and full professorships in Science and Engineering from 1960–2006 (data from reference [33]) as well as percentage of women in various author positions from 1960–2009 as a result of this analysis.

<p>1st and 2nd author positions are listed for papers with at least two authors. Last author percentage is for papers with at least three authors.</p

Authorships and gender composition in the JSTOR network dataset, by decade.

<p>Shaded bars represent male authorships, unshaded bars represent female authorships. The black line indicates the fraction of authorships that are women, the red line indicates the fraction of first authorships that are women, and the blue line indicates the fraction of last authorships that are women.</p

Gender composition from 1990–2011 for disciplines (i.e., groups at the first level of hierarchical clustering) with at least 5,000 authorships.

<p>Gender composition from 1990–2011 for disciplines (i.e., groups at the first level of hierarchical clustering) with at least 5,000 authorships.</p