Metrics for graph comparison: A practitioner’s guide

Wills, Peter R.; Meyer, François G.

doi:10.1371/journal.pone.0228728

Cited by 112 publications

(81 citation statements)

References 86 publications

(127 reference statements)

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“…In the following we approach this question by methods of spectral graph theory (Gu et al. 2016 ; Wilson and Zhu 2008 ; Wills and Meyer 2020 ), adding to the applications of spectral analysis of evolutionary graphs (Richter 2017 , 2019a , b , 2020 ; Allen et al. 2019 ).…”

Section: Resultsmentioning

confidence: 99%

“…The principal quantity for assessing structural properties of the graph is the spectral gap (Hoffman et al. 2019 ; Wilson and Zhu 2008 ; Wills and Meyer 2020 ). Figure 6 gives the spectral gap over for the quartic graphs of order and the cubic graphs with as a scatter plot, for results of the remaining graphs, see the Appendix, Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Small values of imply large mixing times, bottlenecks, clusters and low conductance (Banerjee and Jost 2008 , 2009 ; Hoffman et al. 2019 ; Wills and Meyer 2020 ). Moreover, a low spectral gap indicates path-like graphs which are rather easy to divide into disjointed subgraphs by removing edges or vertices.…”

Section: Resultsmentioning

confidence: 99%

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Spectral analysis of transient amplifiers for death–birth updating constructed from regular graphs

Richter

2021

J. Math. Biol.

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A central question of evolutionary dynamics on graphs is whether or not a mutation introduced in a population of residents survives and eventually even spreads to the whole population, or becomes extinct. The outcome naturally depends on the fitness of the mutant and the rules by which mutants and residents may propagate on the network, but arguably the most determining factor is the network structure. Some structured networks are transient amplifiers. They increase for a certain fitness range the fixation probability of beneficial mutations as compared to a well-mixed population. We study a perturbation method for identifying transient amplifiers for death–birth updating. The method involves calculating the coalescence times of random walks on graphs and finding the vertex with the largest remeeting time. If the graph is perturbed by removing an edge from this vertex, there is a certain likelihood that the resulting perturbed graph is a transient amplifier. We test all pairwise nonisomorphic regular graphs up to a certain order and thus cover the whole structural range expressible by these graphs. For cubic and quartic regular graphs we find a sufficiently large number of transient amplifiers. For these networks we carry out a spectral analysis and show that the graphs from which transient amplifiers can be constructed share certain structural properties. Identifying spectral and structural properties may promote finding and designing such networks.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Spectral analysis of transient amplifiers for death–birth updating constructed from regular graphs

Richter

2021

J. Math. Biol.

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“…To test whether global network reorganization took place after overlearning, the distance measures 'edit distance' and 'Deltacon' were calculated. Edit distance computes additions or deletions of connections between two graphs 129 . The edit distance matrix was defined as:…”

Section: Networkmentioning

confidence: 99%

“…Where A and A' are the adjacency matrices for graphs G (session one) and G' (session two) respectively, and is the pairwise edit distance 129 . Since session one and two shared node identity, this pairwise application was applicable.…”

Section: Networkmentioning

confidence: 99%

Reorganization of the neurobiology of language after sentence overlearning

Skipper

Aliko

Brown

et al. 2020

Preprint

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There is a widespread assumption that there are a static set of ‘language regions’ in the brain. Yet, people still regularly produce familiar ‘formulaic’ expressions when those regions are severely damaged. This suggests that the neurobiology of language varies with the extent of word sequence learning and might not be fixed. We test the hypothesis that perceiving sentences is mostly supported by sensorimotor regions involved in speech production and not ‘language regions’ after overlearning. Twelve participants underwent two sessions of behavioural testing and functional magnetic resonance imaging (fMRI), separated by 15 days. During this period, they repeated two sentences 30 times each, twice a day. In both fMRI sessions, participants ‘passively’ listened to those two sentences and novel sentences. Lastly, they spoke novel sentences. Behavioural results confirm that participants overlearned sentences. Correspondingly, there was an increase or recruitment of sensorimotor regions involved in sentence production and a reduction in activity or inactivity for overlearned sentences in regions involved in listening to novel sentences. The global network organization of the brain changed by ∼45%, mostly through lost connectivity. Thus, there was a profound reorganization of the neurobiology of speech perception after overlearning towards sensorimotor regions not considered in most contemporary models and away from the ‘language regions’ posited by those models. These same sensorimotor regions are generally preserved in aphasia and Alzheimer’s disease, perhaps explaining residual abilities with formulaic language. These and other results warrant reconsidering static neurobiological models of language.

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