What is a complex graph?

Kim, Jong-Kwang; Wilhelm, Thomas

doi:10.1016/j.physa.2008.01.015

Cited by 193 publications

(158 citation statements)

References 37 publications

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“…In the past decade or so, two measures have been proposed in the statistics literature for measuring complexity of a given unweighted graph (a graph whose edges have only two value, 0 and 1) with JV nodes (Kim and Wilhelm, 2008). They are described in Section 2.6.…”

Section: Measuring Complexity Of Networkmentioning

confidence: 99%

“…The Graph Index Complexity, C r , indicates the diversity or heterogeneity of distribution of the edges over all the nodes, defined as (Kim and Wilhelm, 2008 …”

Section: Graph Index Complexity C Rmentioning

confidence: 99%

“…In this research, the complexity is computed using two different measures: Graph Index Complexity and Efficiency Complexity (Kim and Wilhelm, 2008;Bello-Orgaz et al, 2012). These measures have been selected because they can measure the global complexity of the brain functional connectivity network after quantifying the constructed network using synchronization methods (Besio et al, 2011;Han et al, 2011;Serletis et al, 2013;Rangaprakash et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

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Complexity of functional connectivity networks in mild cognitive impairment subjects during a working memory task

Ahmadlou

Adeli

Bajo

et al. 2014

Clinical Neurophysiology

126

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HIGHLIGHTS• We use magneto-encephalograms in patients with mild cognitive impairment (MCI).• We investigate complexity of functional connectivity network of MCI patients using two different measures: Graph Index Complexity and Efficiency Complexity.• Efficiency Complexity is superior to Graph Index Complexity and its value at theta band can be used for diagnosis of MCI. ABSTRACT Objectives:The objective is to study the changes of brain activity in patients with mild cognitive impairment (MCI). Using magneto-encephalogram (MEG) signals, the authors investigate differences of complexity of functional connectivity network between MCI and normal elderly subjects during a working memory task. Methods: MEGs are obtained from 18 right handed patients with MCI and 19 age-matched elderly participants without cognitive impairment used as the control group. The brain networks' complexities are measured by Graph Index Complexity (C r ) and Efficiency Complexity (Q). Results:The results obtained by both measurements show complexity of functional networks involved in the working memory function in MCI subjects is reduced at alpha and theta bands compared with subjects with control subjects, and at the theta band this reduction is more pronounced in the whole brain and intra left hemisphere. Conclusions: C e would be a better measurement for showing the global differences between normal and MCI brains compared with C r . Significance: The high accuracy of the classification shows C e at theta band can be used as an index for assessing deficits associated with working memory, a good biomarker for diagnosis of MCI.

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Section: Measuring Complexity Of Networkmentioning

confidence: 99%

“…The Graph Index Complexity, C r , indicates the diversity or heterogeneity of distribution of the edges over all the nodes, defined as (Kim and Wilhelm, 2008 …”

Section: Graph Index Complexity C Rmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Complexity of functional connectivity networks in mild cognitive impairment subjects during a working memory task

Ahmadlou

Adeli

Bajo

et al. 2014

Clinical Neurophysiology

126

View full text Add to dashboard Cite

show abstract

“…For finalizing this section, we also reproduce the so-called offdiagonal complexity (OdC) [65] that is based on determining the entropy of the offdiagonal elements of the vertex-vertex link correlation matrix [65,66]. Let G = (V, E) be a graph and let (c ij ) ij be the vertex-vertex link correlation matrix, see [65].…”

Section: Other Information-theoretic Network Measuresmentioning

confidence: 99%

“…Let G = (V, E) be a graph and let (c ij ) ij be the vertex-vertex link correlation matrix, see [65]. Here c ij denotes the number of all neighbors possessing degree j > i of all vertices with degree i [66].k := max v∈V k v stands for the maximum degree of G. If one defines [66] a |V | :=k…”

Section: Other Information-theoretic Network Measuresmentioning

confidence: 99%