Shannon entropy of brain functional complex networks under the influence of the psychedelic Ayahuasca

The entropic brain hypothesis holds that the key facts concerning psychedelics are partially explained in terms of increased entropy of the brain’s functional connectivity. Ayahuasca is a psychedelic beverage of Amazonian indigenous origin with legal status in Brazil in religious and scientific settings. In this context, we use tools and concepts from the theory of complex networks to analyze resting state fMRI data of the brains of human subjects under two distinct conditions: (i) under ordinary waking state and (ii) in an altered state of consciousness induced by ingestion of Ayahuasca. We report an increase in the Shannon entropy of the degree distribution of the networks subsequent to Ayahuasca ingestion. We also find increased local and decreased global network integration. Our results are broadly consistent with the entropic brain hypothesis. Finally, we discuss our findings in the context of descriptions of “mind-expansion” frequently seen in self-reports of users of psychedelic drugs.

Ayahuasca is a beverage of Amazonian indigenous origin and has legal status in Brazil in religious and scientiic settings 17 . It contains the powerful psychedelic N,N-dimethyltryptamine (DMT), together with harmala alkaloids that are known to be monoamine oxidase inhibitors (MAOIs). he beverage is typically obtained by decoction of two plants from the Amazonian lora: the bush Psychotria viridis, that contains DMT, and the liana Banisteriopsis caapi, that contains MAOIs 18 . DMT is usually rapidly metabolized by monoamine oxidase (MAO), but the presence of MAOI allows DMT to cross the blood-brain barrier and to exert its efects [19][20][21][22][23][24] . Similar to LSD, mescaline and psilocybin [19][20][21][22][23][24] , Ayahuasca can cause profound changes of perception and cognition, with users reporting increase of awareness, lexible thoughts, insights, disintegration of the self, and attentiveness 19,25 . here is growing interest in Ayahuasca, partially due to recent indings showing that it may be efective in treating mental disorders, such as depression 26,27 and behavioral addiction 28,29 . Similar therapeutic potential has also been pointed out for other psychedelics 9,23,[30][31][32][33] .
For analysis, we use tools and concepts from the ield of complex networks, a brief history of which follows. he application of graph theory to phase transitions and complex systems led to signiicant progress in understanding a variety of cooperative phenomena over a period of several decades. In the 1960s, the books by Harary, especially Graph heory and heoretical Physics 34 , introduced readers to powerful mathematical techniques. he chapter by Kastelyn, still considered to be a classic, showed that diicult combinatorial problems of exact enumeration could be attacked via graph theory, including the exact solution of the two-dimensional Ising model (e.g., see Feynman 35 ). In the 1980s, certain families of neural network models were shown to be equivalent to Ising systems, e.g., the Hopield network 36 is a content-addressable memory which is isomorphic to a generalized Ising model 37 . Beginning in the 1990s, new approaches to networks, giving emphasis to concepts such as the node degree distribution, clustering, assortativity, small-worldliness; and network eiciencies, led eventually to what has become the new ield of complex networks 38,39 . hese new tools and concepts [40][41][42] have found successful application in the study of diverse phenomena, such as air transportation networks 43 , terrorist networks 44 , gene regulatory networks 45 , and functional brain networks [46][47][48][49][50] . We approach the human brain from this perspective of complex networks 51,52 .
Ten healthy volunteers were submitted to two distinct fMRI scanning sessions: (i) before and (ii) 40 minutes ater Ayahuasca intake, when the subjective efects become noticeable (the volunteers drank 2.2 mL/kg of body weight and the Ayahuasca contained 0.8 mg/mL of DMT and 0.21 mg/mL of harmine, see Methods section). In both cases, participants were instructed to close their eyes and remain awake and at rest, without performing any task. See Methods for details concerning data acquisition and preprocessing.
Data analysis consists of two main steps. In the irst step, we use fMRI data to generate complex networks to represent the actual functional brain connectivity patterns. In the second step, we use the networks generated in step 1 as inputs and calculate network characteristics as output, using techniques from the theory of complex networks. he Methods section describes both steps in detail. More information about most of the methods used here can be found in refs 4, 53, 54. Figure 1 shows the networks generated from one subject before and ater Ayahuasca intake, for one speciic choice of mean node degree. he spheres represent nodes, with sphere size proportional to the degree of the node. he lower plots show histograms of node degrees.
he main result that we report here is an increase in the Shannon entropy of the degree distribution for the functional brain networks subsequent to Ayahuasca ingestion. We also ind that the geodesic distance increases during the efects of Ayahuasca, i.e. qualitatively the network becomes "larger". More generally, we also ind that these functional brain networks become less connected globally but more connected locally.
he key technical innovation is the measurement of the Shannon entropy of the degree distribution of the complex networks that represent the functional connectivity of the human brain. Moreover, the Shannon entropy is also very closely related to the Boltzmann-Gibbs entropy used in statistical mechanics. Hence, our approach to studying the brain experimentally is grounded in two strong theoretical traditions: graph theory and complex networks on the one hand, and information theory and statistical physics on the other. Our study also represents a signiicant advance for the following additional reasons: (i) our results unveil how Ayahuasca (and likely most other tryptamine psychedelics) alter brain function, both locally and globally; (ii) it is the irst time this speciic approach has been applied to characterize functional brain networks in altered states of consciousness; (iii) our study of Ayahuasca covers all brain regions; and (vi) the method we have developed can be immediately applied to study a variety of other phenomena (e.g., the efects of medication for mental health disorders).

Results
Increase of the Shannon entropy of the degree distributions. We find evidence of significant changes in the functional brain networks of subjects before and ater ingestion of Ayahuasca. Figure 2 shows 2nd as well as 4th central moments of the degree distributions for each subject. he individual values are calculated separately for each network. We ind an increase of variance for all subjects ater Ayahuasca intake and a decrease of kurtosis for almost all of them (6 subjects). hese indings indicate that the degree distributions become less peaked and wider. his behavior is suggestive of an increase of the Shannon entropy for the degree distributions ater Ayahuasca ingestion. Figure 3 shows the average Shannon entropy of the degree distributions as a function of mean degree, considering networks from all subjects, before and ater Ayahuasca intake. A fair comparison of the "before" and "ater" networks is possible by considering the entropy of networks of identical mean degree. We ind an increase in the entropy of the degree distributions ater Ayahuasca ingestion. In order to better evaluate the consistency of this result, we also calculate the average Shannon entropy subject-by-subject, before and ater Ayahuasca (Fig. 4). We ind signiicant increased entropy for all individual subjects.
To ensure that the observed changes in entropy are not due to augmented motion of subjects' heads during the efects of Ayahuasca, we also study the correlation between changes in individual Frame Displacement (FD) 55 SCIENTIFIC REPORTS | : 7388 | DOI: . /s ---against individual changes in entropy. We ind a Pearson correlation coeicient of 0.005 (hence, p-value ≈ 1), between entropy increases and motion (see Supplementary Figure S1). Hence, we discard the possibility that the observed entropy changes are due to augmented motion.
Iso-entropic randomized networks. he degree distribution does not completely deine a network, however it can have great inluence over other network properties. One can quantify this inluence by comparing any given network G to other networks chosen randomly from the ensemble of networks that have exactly the same degree distribution. We refer to such networks as "randomized networks". By deinition, all such randomized networks have the same entropy as the original network G, i.e. they are iso-entropic to G. An eicient way of generating such randomized networks is the Maslov algorithm 56 (see Methods). Whereas entropy is conserved by the Maslov algorithm, the clustering coeicient, geodesic distances and eiciencies are not. By comparing these non-conserved quantities before and ater randomization, we can distinguish efects that Figure 1. Illustrative example of functional brain networks. (a) 3 views of a complex network generated from fMRI data from one subject, before (let) and ater (right) Ayahuasca ingestion (mean node degree 〈k〉 = 30). he spheres represent nodes and sphere size is proportional to the node degree. (b) histograms of node degrees, corresponding to the networks shown in (a). Ater Ayahuasca intake, the distribution is wider, indicating a higher entropy. In (a) we have used the BrainNet Viewer (http://www.nitrc.org/projects/bnv) for visualization.
are due solely to changes in the degree distribution from those that are sensitive to how links are more speciically arranged.
We generate a set of 30 iso-entropic randomized networks for each original network, for all subjects both before and ater Ayahuasca ingestion. Comparison of the original networks with the randomized networks yields important information concerning to what degree the changes in quantities such as geodesic distance, clustering coeicients, and global and local eiciencies can be accounted for by the changes in the degree distributions (see results described below). Figure 5 shows an increase of mean geodesic distance and a decrease of global eiciency ater Ayahuasca ingestion. To determine how much of the change in geodesic distance is due to the change in the degree distribution, we also calculated the geodesic distance and global eiciency for the iso-entropic randomized networks. Note how the values for those networks are quite diferent compared to the non-randomized networks. We conclude that the change in degree distribution cannot explain the entire change Variance and kurtosis of the degree distribution. Mean ± 1 standard deviation calculated over all 16 networks of the degree variance (a) and kurtosis (b), shown for each subject (blue ∇) and ater (green ∆) Ayahuasca ingestion. he individual values for the degree variance and kurtosis are calculated separately for each network. We ind higher variance and (mostly) lower kurtosis ater Ayahuasca, hence the node distributions change shape and become less "peaked". Such behavior is again consistent with (if not suggestive of) a higher Shannon entropy ater Ayahuasca.

Decrease of global integration.
in geodesic distance. he inset in the middle panels shows the change in the normalized mean geodesic distance and global eiciency, which we deine as the ratio D/D rand and similarly for the global eiciency (see refs 4, 53). We see, indeed, that these ratios are not close to zero. If the change in degree distribution could account for all the change in geodesic distance and eiciency, then the change in these ratios would be close to zero. Signiicant changes are also observed at the individual level and are again consistent for all subjects (Fig. 5(e) and (f)). Figure 6 shows an increase of clustering coeicients and local eiciency ater Ayahuasca ingestion. In contrast to the behavior of the metrics discussed above, almost identical changes are seen for iso-entropic networks. his result indicates that the variation in degree distribution can account for most of the change in clustering and local eiciency. he insets in the middle panel show the change in the normalized clustering and local eiciency, which we deine as the ratio C/C rand and similarly for the local eiciency. We see, indeed, that these ratios are close to zero.

Increase of local integration.
Subjective evaluation. he subjective states of the subjects were evaluated using two psychometric scales: the Clinician Administered Dissociative States Scale (CADSS) 57 and the Brief Psychiatric Rating Scale (BPRS) 58 .
We report a signiicant correlation (r = 0.91; p = 0.004) between individual CADSS scores variation and the entropy before Ayahuasca intake (see Supplementary Fig. S2), however one must proceed with caution when interpreting these indigns because of the small number of subjects. he correlations between CADSS score variation and the variation in geodesic distance and global eiciency reach r = 0.71 and r = 0.67, respectively. Although these correlations fall short of our signiicance criterion (r > 0.76, p < 0.05), yet these r values are relatively large when compared with those for the clustering coeicient (r = 0.15) and local eiciency (r = 0.09).

Discussion
Our results reveal that the entropy increases ater Ayahuasca ingestion. he following also increase: geodesic distance, clustering coeicient and local eiciency. However, the global eiciency decreases. Overall, we ind an increase of local integration and a decrease of global integration in the functional brain networks. We interpret these indings in the context of some well understood prototypical classes of networks. Regular lattices have ixed coordination number, hence all nodes have the same degree and the Shannon entropy of the degree distribution is thus zero. In contrast, the entropy is high in networks with broad distributions of degree. he observed increase in entropy ater Ayahuasca ingestion indicates that the degree distribution becomes broader. In the context of the Watts-Strogatz model 59 , clustering and geodesic distance both decrease when highly regular networks are transformed into small-world networks by randomly re-assigning the links. Whereas clustering and geodesic distances decrease with increasing randomness in such models, we ind the opposite behavior for Ayahuasca, i.e., randomness as measured by the Shannon entropy of the node degree distribution increases in parallel with clustering and geodesic distances. Hence, our indings cannot be reduced to simple explanations of greater or lesser randomness. Locally, there is an increase in integration (as measured by network eiciency), but globally there is a decrease in integration. Indeed the increase of geodesic distance and decrease of global  Figure S5). We thus see evidence against the null hypothesis of no change in entropy. Indeed, we ind a signiicant increase in the entropy of the degree distributions ater Ayahuasca ingestion. his entropy increase is the main result that we report.
SCIENTIFIC REPORTS | : 7388 | DOI: . /s ---eiciency ater Ayahuasca intake signify that the functional brain networks are less globally integrated. One possible interpretation of these indings is that the increase of local robustness and the decrease of global integration relect a variation in modular structure of the network. Recent studies have reported the presence of modularity in functional brain networks on several scales 50,60,61 . Modular networks are characterized by the existence of reasonably well-deined subnetworks in which internal connections are denser than connections between distinct subnetworks 50 . However, traditional algorithms [62][63][64] were not able to detect variation on modular structure features between our sets of networks.
Our results are broadly consistent with the entropic brain hypothesis, hence we discuss the latter in the context of our indings. he hypothesis maintains that the mental state induced by psychedelics, which the original authors term "primary-state, " presents relatively elevated entropy in some features of brain organization, compared to the ordinary waking state (termed "secondary") 11 . Although it may be somewhat counter-intuitive that the psychedelic state is considered primary while ordinary consciousness is secondary, their hypothesis is inherently plausible considering that a wider spectrum of experiences is possible with psychedelics than in ordinary consciousness. In this sense, ordinary consciousness can be thought of as a restriction or constrained special case of a more primary consciousness. he hypothesized lower entropy of ordinary consciousness relative to primary consciousness is attributed to this reduction of freedom. In fact, the idea that ordinary consciousness is not primary was previously put forth by Alan Watts to describe what later became widely known as mindfulness 65 . (We emphasize that the terms "primary" and "secondary" are used not as value judgements, but rather to More speciically, we believe that the observed increase in entropy may be related to the temporary removal of the some of the restrictions that are necessary for sustaining ordinary (adult trained) consciousness. With these restrictions temporarily gone, the entropy increases and the mind may become efectively more "free", attaining a more lexible state in which self-referential narratives and thoughts about the past or the future are no longer mentally identiied with the reality that they represent. We emphasize, however, that "correlation is not causation" and that the entropy increases may occurr in parallel with the loss of constraints, rather than bear a direct causal relation to them. hese ideas are further explored in the Supplementary Discussion (see also refs. [80][81][82][83]). Relatively few studies have investigated entropy in brain functional networks, hence additional comments are in order. Tagliazucchi et al. 14 showed that psilocybin (psychedelic present in some species of mushrooms) may be responsible for increases of a diferent entropy measure in functional connectivity of the 4 regions of Default Mode Network (DMN), a relevant functional network related to resting state. Recently, Yao et al. 66 correlated entropy increases in the human brain with age. his study also supports the view that entropy is correlated to brain function (and perhaps also its development). Moreover, in agreement with our results, a study by Schröter et al. 4 similarly suggests that functional network topology may have a central role in consciousness quality. hey investigated the efects on the human brain of the anesthetic propofol, which can induce loss of consciousness 67 . hey reported a decrease of the clustering coeicient, which is strongly inluenced by degree distribution (however, geodesic distance remained unchanged). Very recently, Lebedev et al. 15 and separately Schartner et al. 16 have reported evidence of increases in measures of entropy, the former with LSD and the latter with LSD, psilocybin and ketamine. We briely comment on the limitations of our method: (i) the reduced number of subjects and the fact that all of them were experienced with Ayahuasca do not allow population inferences and do not elucidate whether the efects observed here were only due the acute administration or if previous experience also played a signiicant role; (ii) expectancy and suggestion were not controlled, as placebo was not used; (iii) networks were built upon a number of critical choices, such as the atlas used to partition the brain, the method used to build the correlation matrix, and the cutof thresholds for generating the adjacency matrices from correlation matrices 68,69 , which may afect the inal results; (iv) the chosen range of correlation values automatically limits the networks' behavior to a small-world network. Despite this limitation, it is important to highlight that several studies have consistently demonstrated that brain networks exhibit a small-world behavior 70 .
Finally, we speculate about whether or not our inding of larger mean geodesic distances may have any relation to self-reports of "mind-expansion" by users of psychedelics (see also ref. 16). Could there be a direct relation between entropy increases and the higher creativity reported by users of psychedelics? Such questions merit further investigation. In conclusion, our results are broadly consistent with the hypothesis that psychedelics increase the entropy in brain functions. By calculating the Shannon entropy of the degree distribution of complex networks generated from fMRI data, we have taken a new low-computational-cost approach to investigating brain function under the inluence of psychedelics.

Methods
Data acquisition and preprocessing. The fMRI images were obtained in a 1.5 T scanner (Siemens, Magneton Vision), using an EPI-BOLD like sequence comprising 150 volumes, with the following parameters: TR = 1700 ms; TE = 66 ms; FOV = 220 mm; matrix 64 × 64; voxel dimensions of 1.72 mm × 1.72 mm × 1.72 mm. It also was acquired whole brain high resolution T1-weighted images (156 contiguous sagittal slices) using a multiplanar reconstructed gradient-echo sequence, with the following parameters: TR = 9.7 ms; TE = 44 ms; lip angle 12°; matrix 256 × 256; FOV = 256 mm, voxel size = 1 mm × 1 mm × 1 mm. he images were obtained from 10 healthy right-handed adult volunteers (mean age 31.3, from 24 to 47 years), all who were experienced users of Ayahuasca with at least 5 years use (twice a month) and at least 8 years of formal education. he experimental procedure was approved by the Ethics and Research Committee of the University of São Paulo at Ribeirão Preto (process number 14672/2006). Written informed consent was obtained from all volunteers, who belonged to the Santo Daime religious organization. All experimental procedures were performed in accordance with the relevant guidelines and regulations.
Volunteers were not under medication for at least 3 months prior to the scanning session and were abstinent from cafeine, nicotine and alcohol prior to the acquisition. hey had no history of neurological or psychiatric disorders, as assessed by DSM-IV structured interview 71 . Subjects ingested 120-200 mL (2.2 mL/kg of body weight) of Ayahuasca known to contain 0.8 mg/mL of DMT and 0.21 mg/mL of harmine. Harmaline was not detected via the chromatography analysis, at the threshold of 0.02 mg/mL 7 . Preprocessing steps were conducted in FSL (http://www.ndcn.ox.ac.uk/divisions/fmrib) and include: slice-timing correction, head motion correction and spatial smoothing (Gaussian kernel, FWHM = 5 mm). One volunteer was excluded from analysis due to excessive head movement (more than 3 mm in some direction), leaving 9 participants (5 women) to our analysis. All images were spatially normalized to the Montreal Neurologic Institute (MNI152) 72 standard space, using a linear transformation. We also evaluated 9 regressors of non-interest using a General Linear Model (GLM): 6 regressors to movement correction, 1 to white matter signal, 1 to cerebrospinal luid and 1 to global signal. Each volunteer was submitted to fMRI scanning under two distinct conditions: (i) before and (ii) 40 minutes subsequent to Ayahuasca intake. In both cases, volunteers were in an awake resting state: they were requested to stay lying with eyes closed, without performing any task.

Complex network metrics.
For a detailed overview of complex network theory, we refer readers to refs 38,41,49. Each element of a network is known as a node (or vertex), and the relation between a pair of nodes is represented by a connecting link (or edge). Links can have weights associated with them and can be directed or undirected (or, equivalently bi-directional). Nodes connected by a single link are known as nearest neighbors 39 . Non-weighted undirected networks, i.e. those with symmetric and unweighted links are isomorphic to a binary symmetric matrix known as the adjacency matrix. When a pair of nodes i and j are neighbors, the adjacency matrix element is a i,j = 1 and a i,j = 0 otherwise 73,74 . Standard quantities of interest that help to characterize the topology and complexity of networks 49,53 include node degree, geodesic distance, clustering coeicient, and local and global network eiciencies. We are interested here solely in non-weighted undirected networks. Deinitions: (i) he degree k j of a node j is the number of links that it has with other nodes. he degree distribution of a network is the normalized histogram of degrees over all nodes. (ii) A geodesic path between two nodes is the shortest path from one to the other, assuming such a path exists.
he geodesic distance d i,j between nodes i and j is the number of links in the geodesic path. If there is no such path, the geodesic distance is deined as ininite. Given a network G with N nodes, the mean geodesic distance is given by where k i is the degree of node i and a is the adjacency matrix element. (iv) he eiciency, typically deined as the reciprocal of the harmonic mean of geodesic distances, quantiies the inluence of the topology on lux of information through the network. Eiciency can be global as well as local. We deine global eiciency as and local eiciency as where g i are the subnetworks formed by neighbors of node i and n i is the number of nodes of this subnetwork 75 .
In addition to these standard network properties, we also use the Shannon entropy 76 to quantify disorder or uncertainty. Speciically, we calculate the Shannon entropy functional of the distribution of node degrees. Let P be the normalized probability distribution for node degree k, i.e. ∑ k P(k) = 1. We deine the Shannon entropy S[P] of the degree distribution P(k) for a network with N nodes by: Oten the logarithm of base 2 is used 77 (e.g., in computer science), but we use the natural logarithm instead, so the entropy values shown are in natural information units rather than in bits.
Maslov algorithm for generating randomized networks. Given G, one can select two non-overlapping pairs (i, j) and (m, n) of linked nodes, then unlink them, and cross-link the pairs according to (i, m) and (j, n).
If this process is repeated many times, the links become randomized, but the degree of each node remains the same 56 . Hence the entropy of the degree distribution is also a conserved quantity.
Calculation of correlation matrix for brain regions. We segmented the brain images into 110 brain regions according to the Harvard-Oxford cortical and subcortical structural atlas (threshold of >25%, using FMRIB Sotware Library, www.fmrib.ox.ac.uk/fsl). Six regions had to be excluded from further analysis, as they were not sampled for all subjects, due to technical limitations during image acquisition. For each of the 104 regions, an averaged fMRI time series was computed from all voxels (a voxel is a 3D image block, analogous to the 2D pixel). within that region using Marsbar (SPM toolbox). To reduce confounders, we applied a band-pass ilter (≈0.03-0.07 Hz) using the maximum overlap wavelet transform (MODWT) with a Daubechies wavelet to divide the signal into 4 scales of diferent frequency bands. In keeping with the literature 4,54 , that point that resting state typically leads to low frequency (≈0.01 to 0.1 Hz) 78 , we choose scale 3. We then calculated the Pearson correlation between these wavelet coeicients from all possible pairs, thus obtaining a 104 × 104 correlation matrix to represent each sample. We considered only correlation matrix elements that resulted in p < 0.05 in the hypothesis test. hat is, we zero correlation matrix elements with non-reliable values (p ≥ 0.05).

Construction of complex networks from fMRI images.
A correlation matrix uniquely may deine a weighted network. Nonetheless, we are interested in generating non-weighted networks. Hence, we need a function that maps correlation matrices to adjacency matrices. We use a thresholding function for this purpose. Given a correlation matrix, we obtain the adjacency matrix by applying a threshold to the absolute value of the elements of the correlation matrix. Speciically, if the absolute value of the correlation matrix element |c i,j | is larger than a deined threshold η, then a link is assumed and the adjacency matrix element is taken to be 1 (i.e., a i,j = 1), while otherwise there is no link (a i,j = 0). In order to obtain better statistics, we choose not a single value of η but a range of values instead. hen we analyze the behavior of the network properties over this range. Using this approach, we create a number of networks for each fMRI sample, all with the same number of nodes (104 nodes). For each of these networks, we choose η such that the density of links is the same before and ater Ayahuasca intake. We choose a range for the mean network degree to ensure the networks were fully connected but also relatively sparse. For this purpose, we adopt the following criteria: (i) the lowest correlation threshold (corresponding to maximum mean degree) must ensure that the networks have lower global eiciency and greater local eiciency than its randomized version. hese criteria also ensure small-world behavior of the networks 79 (according to the deinition of Watts and Strogatz 59 ). (ii) the upper correlation threshold (minimum mean degree) must ensure fully connected graphs and also guarantee that the networks obey the sparsity condition 〈k〉 > 2lnN, where N = 104 is the number of nodes. Since the quantity 2lnN never exceeds 10, our maximum threshold condition (minimum mean degree) was determined by the requirement for obtaining fully connected graphs. (A properly deined large N limit of this condition would be equivalent to the percolation threshold).
We choose common upper and lower thresholds for all correlation matrices (see Supplementary Fig. S3 for more details). hese criteria are identical to those adopted by refs 4, 54. In order to obtain the same threshold SCIENTIFIC REPORTS | : 7388 | DOI: . /s ---range for all subjects, it was necessary to exclude two of them from the analysis, since there is no threshold range common between them and the other subjects. Data from a third subject was also excluded due to excessive head movement. Following the criteria described above, the threshold range is set to 0.25 ≤ η ≤ 0.43. We generate networks with mean degree in the range 24 ≤ 〈k〉 ≤ 39. We have shown in Figs 3, 5 and 6 network properties as a function of mean degree in increments of ∆〈k〉 = 1, for 16 diferent values of mean degree. We choose mean degree as the independent parameter instead of the correlation threshold because, unlike the latter, the mean degree is a network property. Despite the mean degree being a monotonic function of correlation threshold for all subjects, there is no a priori reason to expect universal behavior of network properties such as the entropy and geodesic distance (before vs. ater Ayahuasca) as a function of the correlation threshold since the latter is not a network property (see Supplementary Fig. S3).
In summary, we have 7 human subjects suitable for both conditions (before and ater ingestion). he resulting sets of networks allow 16 diferent comparisons (i.e. of difering mean degrees) for each subject before and ater Ayahuasca ingestion. We calculate the topological measurements (using the Brain Connectivity Toolbox for Matlab 49 ).

Statistical testing.
Comparisons between the two conditions (i.e., before and ater Ayahuasca) are obtained from paired-sample Student's t-tests. he p-values shown in Figs 3, 4, 5 and 6 are as follows: values p < 0.05 in bold and p < 0.005 indicated by asterisks (*). he implicitly assumed null hypothesis is that the diference of the paired values are normally distributed with zero mean.