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Aug 31, 2015 05:08 AM | Alfonso Nieto-Castanon - Boston University
RE: Correlations of graph theory measures
Hi Roger,
That is an interesting observation. I believe this reflects an expected trade-off between global and local efficiency when considering fixed-cost networks. In particular, networks that have comparatively more long-range connections -e.g. more similar to random networks- tend to have higher global efficiency at the cost of lower local efficiency, while networks that have comparatively more local/neighboring connections -e.g. more similar to a lattice- tend to have higher local efficiency at the cost of lower global efficiency. The cost-value threshold that shows small-world regime for graph-theory analyses is determined globally across subjects (we choose a fixed cost value where, across subjects, we find typically high global and local efficiency values in the resulting subject-specific networks). This means that looking at the distribution of local and global efficiency measures at the chosen fixed-cost value, we would expect to see that the center/average of this distribution is relatively high in both the local and global efficiency coordinates. The negative correlations that you describe, instead, characterize the covariance/shape of this distribution (indicating a longer axis along the negative-diagonal direction), rather than its centroid position. Just out of curiosity I checked on an unrelated dataset (HCP, 497 subjects, network of speech-related areas) and I do see similarly high negative correlations between local and global efficiency measures, so I do not believe this is artifactual but probably describes an interesting principal axis of variability across subjects. Perhaps looking beyond normal populations and/or a wider age-range one would expect to see larger variability along the positive-axis as well (resulting in decreased negative correlations)?. Also I imagine that perhaps networks defined based on absolute correlation thresholds instead of fixed-cost thresholds are likely to exhibit less of this effect. In any way, let me know your thoughts.
Best
Alfonso
Originally posted by Roger Beaty:
That is an interesting observation. I believe this reflects an expected trade-off between global and local efficiency when considering fixed-cost networks. In particular, networks that have comparatively more long-range connections -e.g. more similar to random networks- tend to have higher global efficiency at the cost of lower local efficiency, while networks that have comparatively more local/neighboring connections -e.g. more similar to a lattice- tend to have higher local efficiency at the cost of lower global efficiency. The cost-value threshold that shows small-world regime for graph-theory analyses is determined globally across subjects (we choose a fixed cost value where, across subjects, we find typically high global and local efficiency values in the resulting subject-specific networks). This means that looking at the distribution of local and global efficiency measures at the chosen fixed-cost value, we would expect to see that the center/average of this distribution is relatively high in both the local and global efficiency coordinates. The negative correlations that you describe, instead, characterize the covariance/shape of this distribution (indicating a longer axis along the negative-diagonal direction), rather than its centroid position. Just out of curiosity I checked on an unrelated dataset (HCP, 497 subjects, network of speech-related areas) and I do see similarly high negative correlations between local and global efficiency measures, so I do not believe this is artifactual but probably describes an interesting principal axis of variability across subjects. Perhaps looking beyond normal populations and/or a wider age-range one would expect to see larger variability along the positive-axis as well (resulting in decreased negative correlations)?. Also I imagine that perhaps networks defined based on absolute correlation thresholds instead of fixed-cost thresholds are likely to exhibit less of this effect. In any way, let me know your thoughts.
Best
Alfonso
Originally posted by Roger Beaty:
Hi all,
I ran graph analysis of resting-state data in a sample of 300 healthy subjects using AAL ROIs. In looking at the correlations of the graph measures across the whole network, global efficiency and clustering coefficient show a large negative correlation (r = -.75). Is this normal? I would expect a large positive correlation, since small-world networks typically show high efficiency and clustering.
Thanks,
Roger
I ran graph analysis of resting-state data in a sample of 300 healthy subjects using AAL ROIs. In looking at the correlations of the graph measures across the whole network, global efficiency and clustering coefficient show a large negative correlation (r = -.75). Is this normal? I would expect a large positive correlation, since small-world networks typically show high efficiency and clustering.
Thanks,
Roger
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| Title | Author | Date |
|---|---|---|
| Roger Beaty | Aug 30, 2015 | |
| Alfonso Nieto-Castanon | Aug 31, 2015 | |