Healthcare networks power law with cutoff properties.

<p>We analyzed PPN and OON for adherence to power a law distribution starting from a minimum vertex degree, (<i>x</i>_<i>min</i>), using the method of Clauset, et al [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175876#pone.0175876.ref060" target="_blank">60</a>] with <i>τ</i> = 365 days. The orange points are the CDF of the vertex degree, and the blue dashed line is the power law fit of the CDF given <i>x</i>_<i>min</i> and <i>α</i>.</p

Effect of edge weight censoring^‡.

<p>Effect of edge weight censoring<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175876#t003fn002" target="_blank">^‡</a>.</p

Network vertex degree distribution by algorithm for <i>τ</i> = 365 days.

<p>Network vertex degree distribution by algorithm for <i>τ</i> = 365 days.</p

Variation in provider community identification.

<p>We analyzed undirected Provider-Provider networks constructed with the trace-route, sliding frame and binning algorithms for <i>τ</i> = 365 days, and censored for edge weights ≤ 11. Provider-Provider community teams identified for providers within NY State from each network using the Girvan-Newman modularity community finding algorithm [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175876#pone.0175876.ref026" target="_blank">26</a>] implemented in <i>Mathematica</i>. Each provider was assigned to only one community. (A) Provider densities. Hexagonal bins show the counts of providers that were members of any community within each geographic region color coded by range. Note the different geographic density patterns for each method. (B) Histogram of number of providers per community. Note the large number of communities (<i>n</i>) in each histogram, with the majority having only 2 providers. Community sizes, compositions and number differed between all 3 methods. (C) Shows the five largest communities identified in each network.</p

Betweenness centrality <i>C</i>′<i>_β</i> of healthcare networks by algorithm for <i>τ</i> = 365 days betweenness centrality was calculated for all networks using the Oracle PGX algorithm.

<p>Results are displayed with algorithmic binning of <i>C</i>′<i>_β</i> = <i>C^β</i> / (<i>N</i> − 1)(<i>N</i> − 2) for directed graphs produced by the sliding frame and trace-route algorithms, and <i>C</i>′<i>_β</i> = 2<i>C^β</i> / (<i>N</i> − 1)(<i>N</i> − 2) for undirected networks produced by the binning algorithm. All plots are scaled in the y-axis to frequency, allowing direct comparison of centralities. Note that edge-weight censoring (excluding edges with Ω_{<i>v</i>_<i>j</i> → <i>v</i>_<i>k</i>} ≤ 11) markedly changes the centrality distribution of all networks.</p

Network vertex counts, edge counts and density as a function of the sampling frame interval <i>τ</i>.

<p>Vertex counts, edge counts and network density plotted for provider and organization networks for the binning (red), trace-route (orange) and sliding frame (blue) algorithms for <i>τ</i> = 30, 60, 90, 180, and 365 days. Solid lines represent networks where vertices were included if the minimum edge weight > = 1, while dashed lines represent censoring where only edges with a minimum edge weight > = 11 are included. The latter is the current standard for aggregate provider network data release by the Center for Medicare Services so that individual patients cannot be identified by a unique combination of providers sharing only a single patient.</p