Datasets

The data used in our research consist of the brain connectome of Drosophila melanogaster in two stages, i.e., larval and adult ones.

We extracted the larval connectome following the instructions given in Winding et al. (2023). The data for this connectome are provided as a collection of four adjacency matrices representing the pre-synaptic and post-synaptic connections between dendrites and axons of neurons. Specifically, the four adjacency matrices are as follows: (i) the dendrite-dendrite matrix, which represents the connections between the dendrites of the two neurons involved; (ii) the axon-dendrite matrix, which represents the connections between the axon of the pre-synaptic neuron and the dendrite of the post-synaptic neuron; (iii) the dendrite-axon matrix, which represents the connections between the dendrite of the pre-synaptic neuron and the axon of the post-synaptic neuron; (iv) the axon-axon matrix, which represents the connections between the axons of the two neurons involved. In the matrices above, each pair of connected neurons is associated with a weight that represents the number of synapses involved in the connection as a proxy for functional strength. In addition, the dataset provides a further matrix, called ALL-ALL, which merges the four matrices presented above into one.

We extracted the adult connectome following the instructions given in Lin et al. (2024) and companion papers (Dorkenwald et al., 2024; Schlegel et al., 2024). In this dataset, the connections between neurons are represented by the adjacency matrix of a network without distinguishing between different types of connections. This matrix is therefore similar to the larval ALL-ALL matrix. Similar to the larval case, each pair of connected neurons is associated with a weight representing the number of synapses involved in the connection.

Due to the slight differences between the two datasets, and to perform a uniform analysis of the connectome for both larval and adult stages of Drosophila, we only used the ALL-ALL matrices as connection type can account for unique synaptic characteristics. This additionally allows us to focus on the presence or absence of a connection between a pair of neurons without taking into account the possible presence of multiple connections between them. Such information would only be available for the larva, making it useless for a uniform study of the larval and adult connectomes. Also, in order not to go too low in abstraction, given a connection between two neurons, we did not consider the number of synapses involved and thus the weight of the connection, but simply its existence.

Exploring Larval and Adult Connectomes

Larval stage neuronal groups are listed in Table 1. The larva dataset included 346 neurons not associated with any neuronal group (“annotation”). These unclassified neurons were not taken into account when making explicit considerations about neuronal groups. Adult stage neuronal groups are listed in Table 2.

Table 1 Larval stage neuronal groups (adapted from Winding et al. (2023)). For each group, the name and description are providedTable 2 Adult stage neuronal groups (adapted from Schlegel et al. (2024)). For each group, the name and description are provided

As a first step in our study, we performed an Exploratory Data Analysis on the larval and adult connectomes to compare some of their basic features considering the theory of complex network analysis (Table 3).

Table 3 Values of some of the basic features of the Drosophila connectome. For each feature, the values of the larva and adult are provided

We unravel the following changes in the connectome of the adult stage compared to the larval stage: (i) the number of neurons and connections increases significantly (by two orders of magnitude for neurons and one order of magnitude for connections); (ii) the average node degree and the average clustering coefficient decrease; (iii) the density decreases significantly (by two orders of magnitude); and (iv) the average path length and diameter remain essentially constant. Based on the analysis of these basic features, where the average node degree, density, and clustering coefficient decrease, we hypothesize that growth in connections is less than growth in neurons, i.e. nodes in the adult connectome tend to differentiate more forming more selective connections that aim to link specific neuronal groups with each other. The trend of these basic features observed in Drosophila connectomes differs greatly from that observed in other types of networks (e.g., social, technological, and information networks), where density increases and diameter decreases as networks grow (Leskovec et al., 2005).

The degree assortativity is moderately positive in the case of larva and essentially null in the case of adult, whereas the maximum strongly connected components in larval and adult connectomes show very similar behavior. In both cases, we observe the presence of a large maximum (strongly) connected component including 95.19% of the nodes of the larva and 89.25% of the nodes of the adult. This implies that information can easily flow between all or almost all neurons in the larval and adult connectomes.

Centrality Measures of Larva and Adult Connectomes

The degree centrality was the only one used in Lin et al. (2024) to define the rich club neurons in adult Drosophila. In Fig. 2, we show the distribution of degree centrality, in both normal and log-log scales, for the networks associated with the larval (Fig. 2A) and the adult (Fig. 2B) Drosophila connectomes. The distribution of degree centrality in the adult follows a very steep power law, with very few neurons having a very high number of connections and many neurons having a low number of connections. In the larval distribution, we can see the presence of a bell-shaped distribution superimposed by a second bell-shaped distribution and followed by a tail that includes a low number of nodes with very high degree centrality values. This means that in the larva we have many neurons with a medium-low number of connections and few neurons with a high number of connections. Comparing the tails of the larva and adult, we can see that the adult’s tail is much larger, indicating a much greater variability in the number of connections of the neurons of the adult.

Fig. 2

A Distribution of degree centrality, in both normal (i) and log-log scales (ii), for the network associated with the larval connectome. B As in A for the adult connectome. The degree centrality distribution in the adult follows a steep power law. The larval distribution is a bell-shaped curve superimposed by a second bell-shaped curve, followed by a tail

In Fig. 3, we show the distribution of the values of the closeness centrality in the network. Note that in both cases there is a bell-shaped distribution, which is typical for closeness centrality (Tsvetovat & Kouznetsov, 2011). The distribution of the larva is more regular, while that of the adult resembles more the superposition of three bell-shaped curves with gradually increasing heights. Both distributions have a long tail, but the larval distribution is shifted more to the right than the adult one. Both distributions show that few neurons have a very high closeness centrality, many neurons have a medium closeness centrality, and few neurons have a low closeness centrality. Since the closeness centrality of a node in a network is inversely proportional to its average distance from the other nodes in the network (see “Centrality Measures of Larva and Adult Connectomes” section), Fig. 3 tells that, in both the larva and the adult, a small number of neurons are connected to other neurons by short paths, a few are connected by long paths, and the majority are connected by paths that are neither too short nor too long.

Fig. 3

A Distribution of closeness centrality for the network associated with the larval connectome. B As in A for the adult connectome. Both graphs show that few neurons have a very high closeness centrality, many neurons have a medium closeness centrality, and few neurons have a low closeness centrality

The betweenness centrality distributions for the larva and adult are shown in Fig. 4. Both distributions follow a power law, with it being steeper for the adult. The larval distribution has also some irregularities on the left side. The power law distribution characterizing these curves tells us that in the larval and adult connectome, there are many neurons not strategic for connecting different portions of the brain, while there is a small number of neurons very strategic for this task.

Fig. 4

A Distribution of betweenness centrality, in both normal (i) and log-log scales (ii), for the network associated with the larval connectome. B As in A for the adult connectome. Both distributions follow a power law, with it being steeper and more regular for the adult

The last classical centrality we consider is the eigenvector centrality (Fig. 5). Both distributions follow a power law and as in the previous cases, the adult distribution is steeper than the larval one. Both in the adult and the larval connectomes there are many unimportant neurons because they are linked with few connections to other unimportant neurons. At the same time, there are a few very important neurons because they are linked with many connections to other important or very important neurons.

Fig. 5

A Distribution of eigenvector centrality, in both normal (i) and log-log scales (ii), for the network associated with the larval connectome. B As in A for the adult connectome. Both distributions follow a power law, with it being steeper for the adult

To complement the visual inspection of Figs. 2–5 and rule out scale effects, we quantitatively compared the centrality distributions of the larva and adult using non-parametric two-sample tests. First, we normalized the degree centrality and betweenness centrality values by dividing each value by their respective maximum possible value. The other centrality values were already normalized. Next, we performed an additional normalization step to convert from the normal scale to the logarithmic scale. To this end, for each value x of each centrality, we calculated \(\log _(1+x)\). At this point, we applied the Kolmogorov–Smirnov (Table 4) and Mann–Whitney U tests (Table 5) with Benjamini–Hochberg correction to all the resulting centrality values. Both of them confirm that the distributions of centrality values for the larva and adult are very different.

Table 4 Values of the statistic (D) and p-value for the normalized centrality value distributions of the larva and adult - Kolmogorov-Smirnov test. They confirm that the distributions of centrality values for the larva and adult are very differentTable 5 Values of the statistic (U), p-value and Cliff’s delta (\(\delta \)) for the normalized centrality value distributions of the larva and adult - Mann–Whitney U test. They confirm that the distributions of centrality values for the larva and adult are very different

The presence of a negative \(\delta \) with a very high absolute value for degree (resp., closeness, betweenness, eigenvector) centrality indicates that the neurons of the larva have much higher degree (resp., closeness, betweenness, eigenvector) centrality than the neurons of the adult. Median values for each normalized centrality for the larva and adult further corroborate on such differences (Table 6). Consistent with the previous results, when we consider the normalized degrees of neurons in the larva and adult together and take those that exceed the 95th percentile, we see that they correspond to all neurons in the larva and 4.8% of the neurons in the adult.

Table 6 Medians for the normalized centrality value distributions of the larva and adult. They confirm that the distributions of centrality values for the larva and adult are very different

To exclude that the differences in degree centrality values derive from the adult connectome having a much larger number of neurons compared to the larval one, we performed a subsampling of the adult neurons by randomly selecting 2,952 neurons as the number of neurons present in the larva. We applied the Kolmogorov-Smirnov test to these degree centrality value distributions. We repeated these two tasks (subsampling of adult neurons and application of the Kolmogorov-Smirnov test) 500 times, calculating the mean and standard deviation of the statistic D, as well as the corresponding p-value, resulting in a mean value of 0.9997, a standard deviation of 0.0010, and a p-value less than 0.001 in all 500 cases. These results confirmed that the differences in degree centrality distribution between the two connectomes are not an artifact related to the different number of neurons, but rather due to their different characteristics.

In summary, in all types of centrality for both larva and adult we observe the presence of a small number of neurons that have an extremely high centrality value. Could it be that neurons with high centrality values are always the same for all types of centrality?

Detecting Power Neurons

Next, we checked if there are any correlations between the different forms of centralities both in the larva and in the adult by relying on Spearman’s correlation coefficient (Zar, 2014) (Figs. 6 and 7).

Fig. 6

Values of the Spearman’s correlation coefficient for the different pairs of centralities in the larva. Color intensity increases with the magnitude of the coefficient (darker cells indicate stronger correlations)

Fig. 7

Values of the Spearman’s correlation coefficient for the different pairs of centralities in the adult. Color intensity increases with the magnitude of the coefficient (darker cells indicate stronger correlations)

We found positive correlations for all the pairs of centralities considered. What is surprising, however, is that such a positive correlation exists even in cases (e.g., when considering degree and closeness centrality) where network analysis generally does not predict it. This reinforces the hypothesis of the existence of nodes characterized simultaneously by high values for all four centralities.

To test the veracity of this hypothesis, for each centrality distribution in the larva and adult we identified the top 20% of neurons with the highest centrality values. In this way, we obtained eight sets of neurons, four for the larva and four for the adult. The 20% threshold is empirical and is related to the following considerations: (i) most distributions follow a power law; (ii) we wanted to narrow the focus to the most important neurons for each centrality, but tried to avoid missing some of them. We calculated the intersection between the different pairs of subsets for the larva and adult (Table 7) and found that the percentage of common neurons for each pair of centralities is very high, which, as mentioned before, is generally not the case in the network analysis pointing to the case of Drosophila as “special” one. Finally, we calculated the percentage of neurons simultaneously belonging to the top 20% of neurons with the highest values for all four centralities and showed that this percentage is 27.46% for the larva and 20.39% for the adult.

Table 7 Percentages of the nodes belonging to the intersection between the top 20% nodes for each pair of centralities. They are very high for each pair of centralities

In the larva, the fraction of power neurons is \(0.2746 \cdot 0.20 = 0.05492\), i.e. the number of power neurons is 162 out of 2,952. Similarly, in the adult, the fraction of power neurons is \(0.2039 \cdot 0.20 = 0.04078\), i.e. the number of power neurons is 5,473 out of 134,181. It should be noted that, out of 134,181 neurons in the adult connectome, 60,848 are marked as rich club neurons.Footnote 1 Our definition of power neurons allows us to identify a significantly smaller number of neurons (i.e., 5,473).

Characterizing Power Neurons

In what follows, we characterize the very small set of power neurons on different trajectories and show that they have some very particular characteristics. One of these trajectories refers to the distribution of power neurons between brain hemispheres and, in this respect, we need to refer to the concept of homologous neurons. Two neurons are considered homologous if the structure of their connections is similar but they belong to two different hemispheres. The authors of Winding et al. (2023) explicitly specified which neurons are homologous in the larval dataset. In contrast, the authors of Lin et al. (2024) did not explicitly specify which neurons are homologous in the adult dataset, but provided a variety of attributes, including superclass, subclass, cell types and hemibrain type. From these attributes, we found a way to identify homologous neurons by specifying that they are those neurons having the same values for all neuronal attributes in the dataset, except of course for the attributes root_id (representing the identifier of the neuron) and side (denoting the hemisphere to which the neuron belongs). Regarding the latter attribute, we note that 9 of the 162 power neurons in the larval connectome and 49 of the 5,473 power neurons in the adult connectome are not labeled as “left” or “right”. For this reason, we decided to exclude these neurons from all analyses that involved distinguishing power neurons in the two hemispheres.

Power Neurons are Strategically Distributed Among Neuronal Groups in the Brain

By comparing the degree of all neurons and power neurons in the larva and adult, we found that the mean and median degree of power neurons is much higher than that of all neurons (Table 8). This is not surprising, considering that a power neuron is defined as a neuron belonging to the intersection of the top 20% of neurons with the highest degree, closeness, betweenness, and eigenvector centrality values. Consequently, power neurons, by their definition, have a very high degree.

Table 8 Mean and median degrees of all neurons and power neurons in the larva and adult. These parameters have much higher values for power neurons than for regular neurons

Interestingly, if we multiply the mean degree of the larval power neurons (175.89) by the number of power neurons (162), we find that there are 28,494 connections in total. For this calculation, we used the mean instead of the median because multiplying the mean number of connections of each neuron by the number of neurons mathematically gives us the total number of connections in the connectome. This property does not hold if we replace the mean with the median, and the difference is particularly high in scenarios with heavy-tailed degree distributions, such as ours. Considering that the larva has 2,952 neurons, we deduce that there is a very high overlap between the sets of neurons directly connected to a given power neuron, averaging to about 10 different power neurons via an incoming or outgoing arc. A similar situation can be found in the adult, where multiplying the mean degree of power neurons (218.12) by the number of power neurons (5,473), we find that the total number of connections is 1,193,770, while the total number of neurons is 134,181. Thus, on average, each neuron in the adult connectome is linked (through an incoming or outgoing arc) to about 9 different power neurons.

The mean indegree (i.e. the number of arcs incoming to a node) and outdegree (i.e. the number of arcs outgoing from a node) for all neurons are substantially equal. Even the median indegree and outdegree are very close. Instead, when we turn to the power neurons, we observe that the mean and median indegrees are always greater than the corresponding outdegrees. This implies that the average number of neurons from which power neurons receive information is greater than the average number of neurons to which they send information. In other words, power neurons are more information receivers than information providers. Considering that most power neurons are located in specific neuronal groups (see “Exploring Larval and Adult Connectomes” section), i.e. “deep brain” and “learning/memory” in the larva (see Fig. 8) and “central” in the adult (see Fig. 9), we can assume that power neurons receive signals from peripheral sensors, process them in the brain, and stimulate the appropriate peripheral sensors based on the processed information.

We now consider the distribution of power neurons in terms of hemispheres. Table 9 summarizes it and characterizes each power neuron on the basis of the following properties: (i) hemisphere (right / left) in which it is located; (ii) presence or absence of a homolog in the other hemisphere; (iii) type (power neuron / simple neuron) of the possible homolog in the other hemisphere. From the analysis of this table we can see that power neurons are basically equally distributed between the two hemispheres in both the larva and adult. In both cases, there is only a slight prevalence of power neurons in the right hemisphere. A large fraction of power neurons have another power neuron as a homolog; this is the case for 73.20% of power neurons in the larva and 73.89% of power neurons in the adult. The rest of the power neurons usually have a homolog, even if it is not a power neuron. This is always the case in the larva, where there is no power neuron without a homolog, and almost always the case in the adult, where only a small percentage of power neurons (i.e., 3.32%) are without homolog.

Table 9 Distribution and characterization of power neurons between the hemispheres. Power neurons are basically equally distributed between the two hemispheres in both the larva and adult. There is only a slight prevalence of power neurons in the right hemisphere

Continuing this analysis, we considered the distribution of power neurons in the different neuronal groups in the two hemispheres. Figures 8 and 9 show both the number of power neurons per neuronal group/hemisphere and the percentage of neurons that are also power neurons in the corresponding neuronal group/hemisphere.

Fig. 8

Distribution of the larval power neurons by neuronal group and hemisphere. The length of each bar represents the number of power neurons, while the percentages on the top of the bars indicate the fraction of neurons in the neuronal group/hemisphere that are also power neurons. The “deep brain” and “learning/memory” neuronal groups are significantly over-represented in power neurons

Fig. 9

Distribution of the adult power neurons by neuronal group and hemisphere. The length of each bar represents the number of power neurons, while the percentages on the top of the bars indicate the fraction of neurons in the neuronal group/hemisphere that are also power neurons. The “central” and “visual projection” neuronal groups are significantly over-represented in power neurons

As for the larva, it is easy to see that the “deep brain” and “learning/memory” neuronal groups are significantly over-represented in power neurons. In “deep brain”, about 30% of the neurons are power neurons, while in “learning/memory” the fraction of neurons that are power neurons is about 17%. A significant number of power neurons are also present in the “innate” neuronal group, with a smaller presence of about 5%. A small number and percentage of power neurons are distributed in the “pre-output” and “brain outputs” neuronal groups, while no power neurons are present in the “sensory” and “ascending” neuronal groups. This preliminary analysis shows that different neuronal groups are characterized in very different ways with respect to the presence of power neurons. This prompts us to hypothesize about the different roles of power neurons across brain regions.

As for the adult, the highest number of power neurons is in the “central” neuronal group. However, the highest concentration of power neurons is in the “visual centrifugal” and “descending” neuronal groups, where it is about 28% and 27%, respectively. The “visual projection” neuronal group also contains a significant number and proportion of power neurons (about 12%). In contrast, the “sensory”, “ascending”, “optic”, “motor” and “endocrine” neuronal groups are either unrepresented or under-represented in terms of power neurons. Therefore power neurons are more present and characterizing in certain neuronal groups, potentially accumulating and aggregating information from different brain areas.

To address this, we represented power neuron connections in two approaches: In Fig. 10A, a node accounts for each neuronal group and the thickness is proportional to the number of power neurons in that group in the larva. A connection between two nodes exists if at least one of them is a power neuron. In Fig. 10B, connections between two nodes represent connections where both neurons are power neurons. The same applies for the adult (Fig. 11A, B). In both cases, the thickness of the edge is proportional to the number of connections. Extending Figs. 8 and 9, we can now see that the groups with the highest power neuron frequency are the ones that wire together.

Fig. 10

A Larval connectome representing intergroup connectivity mediated by power neurons. Each node represents a neuronal group divided by hemisphere (left or right), and the thickness of each node is proportional to the number of power neurons in that group and hemisphere. Edges represent aggregated neuron-to-neuron connections between the corresponding groups. In each connection at least one endpoint neuron is a power neuron. The edge width encodes connection strength, defined as the number of connections between neurons in the two neuronal groups. Legends serve as a visual guide for estimating node sizes and connection numbers. B As in A but in each connection both endpoint neurons are power neurons

Fig. 11

A Adult connectome representing intergroup connectivity mediated by power neurons. Each node represents a neuronal group divided by hemisphere (left or right), and the size of each node is proportional to the number of power neurons in that group and hemisphere. Edges represent aggregated neuron-to-neuron connections between the corresponding groups. In each connection at least one endpoint neuron is a power neuron. The edge width encodes connection strength, defined as the number of connections between neurons in the two neuronal groups. Legends serve as a visual guide for estimating node sizes and connection numbers. B As in A but in each connection both endpoint neurons are power neurons

Even more interestingly, this also happens between all pairs of neuronal groups in the left and right hemispheres. This confirms the intuition that power neurons are strategic for communication between distant connectome areas. The strongest connections are between left/right partners of the same neuronal groups in “deep brain”, “learning/memory” and “innate”, with “deep brain” and “learning/memory” dominating.

The structure of the graphs in Fig. 10A and B are similar; the most significant but expected change is the complete disconnection of the “ascending” and “sensory” neuronal groups, which not having power neurons could not have connections with the stricter condition characterizing connections in Fig. 10B. It is interesting to note that the connections in the main set still form a complete graph (i.e., a graph in which each pair of nodes is connected by an edge). This implies that, despite their different specializations, all neuronal groups in the main set maintain direct connections with each other. Since these connections involve at least one power neuron (Fig. 10A) or two power neurons (Fig. 10B), we can conclude that this type of neuron plays a fundamental role in ensuring direct communication between the various neuronal groups in the main set. When switching from Fig. 10A to B, the strength of the connections is generally lower, and the number of left/right connections is now greater for the “deep brain” neuronal group instead of the “learning/memory” one. This may be an indicator that power neurons play an even more critical role in the deep brain.

Shifting our analysis to the adult, Fig. 11A shows a less uniform organization than that characterizing the larva. We can still identify a main set of neuronal groups, formed by “central”, “optic”, “visual projection” and “visual centrifugal”, which are more connected than the other ones. In this case, however, this subgraph is not as complete as in the larval case. This means that in the adult, the neuronal groups of the main set are very often directly connected to each other thanks to power neurons. However, compared to the larva, in which all possible pairs of neuronal groups in the main set have a direct connection through one or two power neurons, in the adult there are pairs (for example, the one formed by “visual projection” and “descending”) that are not directly connected to each other through one or two power neurons. Interestingly, the “descending” neuronal group, which is one of the neuronal groups over-represented in terms of power neurons in the adult, is almost exclusively connected to the “central” neuronal group alone, not only by means of intra-hemispheric connections but also through inter-hemispheric ones. Other connections are with the “ascending”, “motor” and “visual centrifugal” neuronal groups. Its counterpart, the “ascending” neuronal group, although under-represented in terms of power neurons, has a similar and symmetric connection structure. In particular, “ascending” neurons are connected to “central”, “descending”, “sensory” and “visual projection” neurons through at least one power neuron. The important property of power neurons to connect distant neurons (e.g., “ascending” and “descending”) is also confirmed in the adult. Note that there is no connection between “optic” and “central” neuronal groups where at least one neuron is a power neuron; in this case, the “visual projection” and “visual centrifugal” neuronal groups seem to act as mediators. In any case, all combinations of possible connections between left / right and “optic” / “visual projection” / “visual centrifugal” neuronal groups via power neurons are present in the resulting graph.

Similar to what we observed for the larva, if we look at the graph with only power neurons (Fig. 11B), the structure of the graph does not change significantly. Clearly, the “motor” and “sensory” neuronal groups are now disconnected, since they have no power neurons. Also, similar to the larva, the connections between the left and right “central” neuronal groups become dominant over the connections between the other neuronal groups.

In summary, we hypothesize that power neurons may play a role in building and maintaining networks of networks within the corresponding connectomes, both larval and adult.

Power Neurons Form a Backbone

We have seen that power neurons are a few nodes with characteristics that make them extremely more powerful than other neurons. It is interesting to see if they also form a backbone, that is, if they tend to prefer contacts with each other over contacts with other nodes. To perform this verification, we decided to compute a number of parameters both in the connectome and in the subnetwork induced by the power neurons, that is, the subnetwork consisting only of the power neurons and the connections between them. The parameters we measured are number of nodes, number of arcs, density, average clustering coefficient, diameter, average shortest path, size of the maximum connected component, average degree, normalized average degree, and degree assortativity.

In Table 10, we report the parameter values obtained for the complete connectome and for the subnetwork of the connectome induced by power neurons alone for both the larva and the adult.

Table 10 Main characteristics and measures of the complete network mapping the connectome and the power neuron subnetwork

Indeed: The density in the induced subnetwork is much higher than in the whole network (specifically, it is 9.73 times higher in the larva and 74 times higher in the adult). The maximum strongly connected component includes a higher fraction of nodes in the induced subnetwork than in the complete network; specifically, for the larva, it includes 100% of the nodes in the induced subnetwork and 95.19% of the nodes in the complete network; for the adult, it includes 99.90% of the nodes in the induced subnetwork and 89.25% of the nodes in the complete network. The average clustering coefficient of the induced subnetwork is higher than in the complete network in both the larva and the adult. The normalized average degree in the induced subnetwork is much higher than in the complete network (in particular, it is about 9.67 times higher in the larva and 50 times higher in the adult). The average shortest path in the induced subnetwork is smaller than that in the complete network, for both the larva and the adult.

A final interesting insight we can derive concerns assortativity. Indeed, we can observe that: In the case of the larva, there is significant assortativity in both the complete network and the induced subnetwork. The assortativity in the complete network indicates that high degree nodes tend to connect with other high degree nodes, and vice versa. Actually, the existence of this phenomenon could already be inferred indirectly from the analyses performed in the previous sections. What is really surprising is that assortativity persists even in the induced subnetwork. Since the latter contains only power neurons, which, as we have seen, generally have high degrees, the persistence of degree assortativity in this network indicates that there might exist a hierarchy among power neurons. In the case of the adult, assortativity is essentially null in both the induced subnetwork and the complete network, and no further insights can be derived.

Connectome Motifs Involving Power Neurons

In this experiment, we wanted to see if there were any connectome motifs (see “Preliminaries” section) in which the core neuron was a power neuron. An example of such a motif is shown in the first row of Table 12 and graphically illustrated in the first network of Fig. 14. It indicates that there is a subnetwork involving neurons from very specific neuronal groups; in particular, there are 202 power neurons of the “central” neuronal group connected by incoming arcs to neurons of the “ascending”, “central”, and “visual projection” neuronal groups, and by outgoing arcs to neurons of the “central” and “descending” neuronal groups. The “central” neuro