Reproducibility and Robustness of Graph Measures of the Associative-Semantic Network

<div><p>Graph analysis is a promising tool to quantify brain connectivity. However, an essential requirement is that the graph measures are reproducible and robust. We have studied the reproducibility and robustness of various graph measures in group based and in individual binary and weighted networks derived from a task fMRI experiment during explicit associative-semantic processing of words and pictures. The nodes of the network were defined using an independent study and the connectivity was based on the partial correlation of the time series between any pair of nodes. The results showed that in case of binary networks, global graph measures exhibit a good reproducibility and robustness for networks which are not too sparse and these figures of merit depend on the graph measure and on the density of the network. Furthermore, group based binary networks should be derived from groups of sufficient size and the lower the density the more subjects are required to obtain robust values. Local graph measures are very variable in terms of reproducibility and should be interpreted with care. For weighted networks, we found good reproducibility (average test-retest variability <5% and ICC values >0.4) when using subject specific networks and this will allow us to relate network properties to individual subject information.</p></div

Group size effect for groups of individual networks.

<p>The average across subjects of the weighted graph measures determined from the individual's network is shown as function of group size. A bootstrapping procedure was used (100 realizations) to randomly group the subjects with increasing group size. For graph measures the relative change (%) to the reference value (which is obtained by averaging across all subjects) are shown. Full lines denote the mean (bold) standard deviation of the metric. Dotted lines represent a relative change of 10%. : global efficiency; : the characteristic path length; : the mean betweenness centrality; : the mean local efficiency and : the mean clustering coefficient.</p

Mean pSI.

<p><i>Bold: Values which are significantly () different from the value obtained from null networks (see text). Italic: .</i></p><p>Mean pSI.</p

The split-half case: the test-retest variability of local graph measures across densities.

<p>The split-half case: the test-retest variability of local graph measures across densities.</p

Intra-subject split-half test-retest variability (%).

<p>The results are shown for binary (over a range of densities) and weighted (w) networks. Error bars refer to the standard deviation across all randomization and subjects. : global efficiency; : the characteristic path length; : the mean betweenness centrality; : the mean local efficiency; : the mean clustering coefficient. Test-retest variabilities significantly () lower than 10% are indicated with *.</p

Group size effect for group based networks.

<p>The effect of group size for networks at a density of 5% (top row), 20% (second row), 45% (third row) and the weighted network (bottom row). A bootstrapping procedure was used (100 realizations) to randomly group the subjects with increasing group size. For graph measures the relative change (%) to the reference value (which is obtained when taking the complete group) are shown. Full lines denote the mean (bold) and standard deviation of the metric. Dotted lines represent a relative change of 10%. : global efficiency; : the characteristic path length; : the mean betweenness centrality; : the mean local efficiency and : the mean clustering coefficient.</p

Robustness to missing nodes for networks with an initial density of 5% (top row), 20% (second row), 45% (third row) and the weighted network (bottom row).

<p>The relative change (%) to the value obtained when taking the intact network as the reference is shown. The nodes were removed based on their significance in the main effect of task (starting with the least significant ones). Dotted lines indicate the 10% interval. Relative changes significantly () lower than 10% in absolute value are indicated with *.</p

Reproducibility at the individual level.

<p>ICC for the global efficiency (), the characteristic path length (), the mean betweenness centrality (), the mean local efficiency () and the mean clustering coefficient (). The results are shown for binary (over a range of densities) and weighted (w) networks. Error bars denote the standard deviation. Values significantly () higher than are indicated with *.</p

Between independent groups: the test-retest variability of local graph measures across densities.

<p>Between independent groups: the test-retest variability of local graph measures across densities.</p

Summary of the main findings.

<p>Summary of the main findings.</p