[may 15th, 2021]
- fdafsdfdas [[fdsafds]] [[fdsafds]] [[fdsaafds]]
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Top keywords (global influence):
Top topics (local contexts):
Explore the main topics and terms outlined above or see them in the excerpts from this text below.
See the relevant data in context: click here to show the excerpts from this text that contain these topics below.
Tip: use the form below to save the most relevant keywords for this search query. Or start writing your content and see how it relates to the existing search queries and results.
Tip: here are the keyword queries that people search for but don't actually find in the search results.
[development]
- [[small-world]] structure is present in most [[social networks]]
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[development]
-
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[fractal dimension of cortical functional connectivity networks]
- Recent evidence suggests that the quantity and quality of conscious experience may be a function of the complexity of activity in the brain and that consciousness emerges in a critical zone between low and high-entropy states. We propose fractal shapes as a measure of proximity to this critical point, as [[fractal dimension]] encodes information about complexity beyond simple entropy or randomness, and fractal structures are known to emerge in systems nearing a [[critical point]]. To validate this, we tested several measures of [[fractal dimension]] on the brain activity from healthy volunteers and patients with disorders of consciousness of varying severity. We used a [[Compact Box Burning algorithm]] to compute the [[fractal dimension]] of cortical functional connectivity networks as well as computing the fractal dimension of the associated adjacency matrices using a 2D box-counting algorithm. To test whether brain activity is fractal in time as well as space, we used the
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[fractal dimension of cortical functional connectivity networks]
[[Higuchi temporal fractal dimension]] on [[BOLD time-series]]. We found significant [[decreases]] in the [[fractal dimension]] between healthy volunteers (n = 15), patients in a minimally conscious state (n = 10), and patients in a vegetative state (n = 8), regardless of the mechanism of injury. We also found significant decreases in adjacency matrix fractal dimension and Higuchi temporal fractal dimension, which correlated with decreasing level of consciousness. These results suggest that [[cortical functional connectivity networks]] display [[fractal character]] and that this is associated with level of consciousness in a clinically relevant population, with higher fractal dimensions (i.e. more complex) networks being associated with higher levels of consciousness. This supports the hypothesis that level of consciousness and system complexity are positively associated, and is consistent with previous EEG, MEG, and fMRI studies.
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[fractal dimension of cortical functional connectivity networks]
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0223812
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[fractal dimension of cortical functional connectivity networks]
-
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[how to calculate the fractal dimension of a complex network]
- Covering a network with the minimum possible number of boxes can
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[how to calculate the fractal dimension of a complex network]
reveal interesting features for the network structure, especially in terms of self-similar
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[how to calculate the fractal dimension of a complex network]
or fractal characteristics. Considerable attention has been recently devoted to this
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[how to calculate the fractal dimension of a complex network]
problem, with the finding that many real networks are self-similar fractals. Here we
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[how to calculate the fractal dimension of a complex network]
present, compare and study in detail a number of algorithms that we have used in
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[how to calculate the fractal dimension of a complex network]
previous papers towards this goal. We show that this problem can be mapped to
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[how to calculate the fractal dimension of a complex network]
the well-known graph coloring problem and then we simply can apply well-established
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[how to calculate the fractal dimension of a complex network]
algorithms. This seems to be the most efficient method, but we also present two other
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[how to calculate the fractal dimension of a complex network]
algorithms based on burning which provide a number of other benefits. We argue
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[how to calculate the fractal dimension of a complex network]
that the presented algorithms provide a solution close to optimal and that another
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[how to calculate the fractal dimension of a complex network]
algorithm that can significantly improve this result in an efficient way does not exist. [[Fractal dimension]] of a complex network https://arxiv.org/pdf/cond-mat/0701216.pdf
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[definitions]
- In [mathematics](https://en.wikipedia.org/wiki/Mathematics), **Hausdorff dimension** is a measure of __roughness__, or more specifically, [[fractal dimension]](https://en.wikipedia.org/wiki/Fractal_dimension), that was first introduced in 1918 by [mathematician](https://en.wikipedia.org/wiki/Mathematician) [Felix Hausdorff](https://en.wikipedia.org/wiki/Felix_Hausdorff).[[2]](https://en.wikipedia.org/wiki/Hausdorff_dimension#cite_note-2)
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[definitions]
-
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[epidemic spreading in scale-free networks]
- The Internet, as well as many other networks, has a very complex connectivity recently modeled by the class of [[scale-free]] networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from computer virus [[infection]] and find the average lifetime and prevalence of viral strains on the Internet. We define a dynamical model for the spreading of infections on [[scale-free]] networks, finding the absence of an [[epidemic threshold]] and its associated critical behavior. This new epidemiological framework rationalize data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks. https://arxiv.org/abs/cond-mat/0010317
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[ideas]
- [[fractal scaling]] means that the network has a fractal dimension while [[scale-free]] means that the nodes' connectivity follows a power-law
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[ideas]
- [[epidemic threshold]] exists in [[homogeneous networks]] and in [[fractal networks]] but not in [[scale-free]]
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[ideas]
- We show that
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[ideas]
the key principle that gives rise to the fractal architecture of [[fractal networks]] is a strong effective “repulsion” ([disassortativity]) between the most connected nodes (hubs) on all
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[ideas]
length scales, rendering them very dispersed. More importantly, we show that a robust network comprised of functional modules, such as a cellular network, necessitates
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[ideas]
a [[fractal topology]], suggestive of an evolutionary drive for their existence.http://www.uvm.edu/pdodds/files/papers/others/2005/song2005b.pdf
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[ideas]
-
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[fractal scale-free networks resistant to disease spread]
- The conventional wisdom is that [[scale-free]] networks are prone to epidemic [[propagation]]; in the paper we demonstrate that, on the contrary, [[disease spreading]] is inhibited in [[scale-free]] [[fractal networks]]. We first propose a novel network model and show that it simultaneously has the following rich topological properties: scale-free degree distribution, tunable clustering coefficient, 'large-world' behavior, and [[fractal scaling]]. Existing network models do not display these characteristics. Then, we investigate the susceptible–infected–removed (SIR) model of the [[propagation]] of diseases in our fractal scale-free networks by mapping it to the bond percolation process. We establish the existence of non-zero tunable epidemic thresholds by making use of the renormalization group technique, which implies that [[power law]] degree distribution does not suffice to characterize the epidemic dynamics on top of scale-free networks. We argue that the epidemic dynamics are
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[fractal scale-free networks resistant to disease spread]
determined by the topological properties, especially the fractality and its accompanying 'large-world' behavior. https://arxiv.org/pdf/0804.3186.pdf
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[fractal scale-free networks resistant to disease spread]
- . In [[homogeneous networks]], there is an existence of nonzero [[infection threshold]], if the spreading rate is above the threshold, the [[infection]] spreads and becomes endemic, otherwise the infection dies outs quickly. However, recent studies demonstrate that the threshold is
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[fractal scale-free networks resistant to disease spread]
absent in heterogeneous [[scale-free]] networks [8,9,10,11]. Thus, it is important
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[fractal scale-free networks resistant to disease spread]
to identify what characteristics of network structure determine the presence
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[fractal scale-free networks resistant to disease spread]
or not of epidemic thresholds.
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[fractal scale-free networks resistant to disease spread]
- Examples of [[fractal networks]] include the [[WWW]], actor collaboration network,
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[fractal scale-free networks resistant to disease spread]
[[metabolic network]], and yeast [[protein interaction network]]
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[fractal scale-free networks resistant to disease spread]
- The [[fractal topology]] is often characterized through two quantities: [[fractal dimension]] dB
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[fractal scale-free networks resistant to disease spread]
and [[degree exponent]] of the boxes dk, both of which can be calculated by the
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[fractal scale-free networks resistant to disease spread]
box-counting algorithm [17,18]
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[fractal scale-free networks resistant to disease spread]
- [[Minimum box-covering method]] is a basic tool to measure [[fractal dimension]] of a network https://journals.aps.org/pre/abstract/10.1103/PhysRevE.78.046109
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[fractal scale-free networks resistant to disease spread]
- Accuracy of the [[ball-covering algorithm]] for [[fractal dimension]] of complex networks and a rank-driven algorithm (https://journals.aps.org/pre/abstract/10.1103/PhysRevE.78.046109)
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[fractal scale-free networks resistant to disease spread]
- in [[fractal networks]] the correlation between [[degree]] and [[betweenness centrality]] of nodes is much [[weaker]] than that in non-fractal networks [19]. In addition, several studies uncovered that [[fractal networks]] are not [[assortative]] [16,20,21]. The peculiar structural nature of fractal networks make them exhibit distinct dynamics. It is known that [[scale-free]] [[fractal networks]] are more [robust] than non-fractal ones against malicious attacks on hub nodes [16,21].
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[fractal scale-free networks resistant to disease spread]
- [[fractal topology]] provides [[protection]] against [[disease spreading]].
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[fractal dimension]
- Many real networks have two fundamental properties, [[scale-free]](https://en.wikipedia.org/wiki/Scale-Free_Networks) property and [[small-world]](https://en.wikipedia.org/wiki/Small-world_network) property.
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[fractal dimension]
- If the [[degree distribution]](https://en.wikipedia.org/wiki/Degree_distribution) of the network follows a [[power-law]](https://en.wikipedia.org/wiki/Power-law), the network is [[scale-free]];
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[fractal dimension]
- if any two arbitrary nodes in a network can be connected in a very small number of steps (short [[average path]]), the network is said to be [[small-world]].
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[may 20th, 2021]
-
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[power law]
-
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[power law]
-
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[emergence of scaling in random networks]
- Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a [[scale-free]] [[power law]] distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
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[fractal weighed networks]
- Fractal weighed networks exhibit the [[small-world]] property. In fact the average shortest path increases logarithmically with the system size (11), hence it is small as the average shortest path of a random network with the same number of nodes and same average degree. On the other hand the clustering coefficient is asymptotically constant (12), thus larger than the clustering coefficient of a random network that shrinks to zero as the system size increases. 8 The self-similarity property of the weighted fractal networks makes them suitable to model real problems involving generic [[diffusion]] over the network coupled with local looses of flow, here modeled via the parameter f < 1. For instance one can think of electrical grids or mammalian lungs, where current or air, flows through power lines or bronchi–bronchioles, submitted to looses of power, or air vessels’ section reduction. In all these cases the induced [[topology]], namely a good choice of f and s, allows any two random
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[fractal weighed networks]
nodes, final power users or alveoli, to be always at finite weighted distance, whatever their physical distance is, and thus to be able to transport current or oxygen in finite time. https://arxiv.org/pdf/0908.4509.pdf
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[scale free]
- When investigating nature we often discard the observed variation and describe its properties in terms of an [[average]], such as the [[mean]] or [[median]] (Gilden, [2001](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B16)). For some objects or processes, however, the average value is a poor description, because they do not have a typical or “characteristic” scale. Such systems are broadly referred to as “[[scale-free]]” (Bassingthwaighte et al., [1994](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B3)). There is growing evidence that physiological processes can exhibit fluctuations without characteristic scales and that this scale-free dynamics is important for their function (Bassingthwaighte et al., [1994](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B3); Bak, [1996](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B2); Goldberger et al., [2002](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B18);
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[scale free]
Stam, [2005](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B51); Ghosh et al., [2008](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B15); He et al., [2010](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B19); West, [2010](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B54)). [[Detrended fluctuation analysis]] ([[DFA]]; Peng et al., [1994](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B45)), a method for analyzing scaling behavior in time series, has played a critical role in this success. We believe, however, that DFA could prove valuable to a wider community of neuroscientists than its current users
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[small-world]
- [[]]
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[human brain functional networks]
- Human brain functional networks demonstrate a fractal [[small-world]] architecture that supports critical dynamics and task-related spatial reconfiguration while preserving global topological parameters. https://www.pnas.org/content/103/51/19518.short
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[treibgut]
- a function that calculates the [[fractal dimension]] of an object embedded in three dimensional space using the [[Minimum box-covering method]] method https://github.com/ChatzigeorgiouGroup/FractalDimension
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[treibgut]
- Other algorithms for calculating [[fractal dimension]]: https://link.springer.com/referenceworkentry/10.1007%2F978-0-387-30440-3_231
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[treibgut]
-
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[social networks]
-
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about about [[backlink propagation]] of [[ideas]]
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[[backlink propagation]] of [[solitude]] and [[desire]]
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bring the universe to the [[network]] of [[consciousness]]
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blocking th universe
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the network is ready to initiate [[propagation]] of [[meaning]]
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bring back the universe
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Semantic Variability Score
— modulates diversity of the discourse network how it works? The score is calculated based on how modular the structure of the graph is (> 0.4 means the clusters are distinct and separate from one another = multiple perspectives). It also takes into account how the most influential nodes are dispersed among those clusters (higher % = lower concentration of power in a particular cluster).
Actionable Insight:
N/A
We distinguish 4 states of variability in your discourse. We recommend that a well-formed discourse should go through every stage during its evolution (in several iterations).
1 - (bottom left quadrant) — biased — low variability, low diversity, one central idea (genesis and introduction stage).
2 - (top right) - focused - medium variability and diversity, several concepts form a cluster (coherent communication stage).
3 - (bottom right) - diversified — there are several distinct clusters of main ideas present in text, which interact on the global level but maintain specificity (optimization and reflection stage).
4 - (left top) — dispersed — very high variability — there are disjointed bits and pieces of unrelated ideas, which can be used to construct new ideas (creative reformulation stage).
Read more in the cognitive variability help article.
1 - (bottom left quadrant) — biased — low variability, low diversity, one central idea (genesis and introduction stage).
2 - (top right) - focused - medium variability and diversity, several concepts form a cluster (coherent communication stage).
3 - (bottom right) - diversified — there are several distinct clusters of main ideas present in text, which interact on the global level but maintain specificity (optimization and reflection stage).
4 - (left top) — dispersed — very high variability — there are disjointed bits and pieces of unrelated ideas, which can be used to construct new ideas (creative reformulation stage).
Read more in the cognitive variability help article.
Shows to what extent you explored all the different states of the graph, from uniform and regular to fractal and complex. Read more in the cognitive variability help article.
You can increase the score by adding content into the graph (your own and AI-generated), as well as removing the nodes from the graph to reveal latent topics and hidden patterns.
You can increase the score by adding content into the graph (your own and AI-generated), as well as removing the nodes from the graph to reveal latent topics and hidden patterns.
× ⁝⁝
Download: TXT Report CSV Report More Options
We provide LDA stats for comparison purposes only. It works with English-language texts at the moment. More languages are coming soon, subscribe @noduslabs to be informed.
positive: | negative: | neutral:
⤓ ? ⤓
Use the Bert AI model for English, Dutch, German, French, Spanish and Italian to get more precise results (slower). Standard model is faster, works for English only, is less precise, and is based on a fixed AFINN dictionary.
?
Main Topical Clusters:
please, add your data to display the stats...
+ ⤓ ? ⤓ The topical clusters are comprised of the nodes (words) that tend to co-occur together in the same context (next to each other).
We use a combination of clustering and graph community detection algorithm (Blondel et al based on Louvain) to identify the groups of nodes are more densely connected together than with the rest of the network. They are aligned closer to each other on the graph using the Force Atlas algorithm (Jacomy et al) and are given a distinct color.
We use a combination of clustering and graph community detection algorithm (Blondel et al based on Louvain) to identify the groups of nodes are more densely connected together than with the rest of the network. They are aligned closer to each other on the graph using the Force Atlas algorithm (Jacomy et al) and are given a distinct color.
Most Influential Elements:
please, add your data to display the stats...
+ ⤓ ↻ ?We use the Jenks elbow cutoff algorithm to select the top prominent nodes that have significantly higher influence than the rest.
Click the Reveal Non-obvious button to remove the most influential words (or the ones you select) from the graph, to see what terms are hiding behind them.
The most influential nodes are either the ones with the highest betweenness centrality — appearing most often on the shortest path between any two randomly chosen nodes (i.e. linking the different distinct communities) — or the ones with the highest degree.
Click the Reveal Non-obvious button to remove the most influential words (or the ones you select) from the graph, to see what terms are hiding behind them.
The most influential nodes are either the ones with the highest betweenness centrality — appearing most often on the shortest path between any two randomly chosen nodes (i.e. linking the different distinct communities) — or the ones with the highest degree.
Network Structure:
N/A
?The network structure indicates the level of its diversity. It is based on the modularity measure (>0.4 for medium, >0.65 for high modularity, measured with Louvain (Blondel et al 2008) community detection algorithm) in combination with the measure of influence distribution (the entropy of the top nodes' distribution among the top clusters), as well as the the percentage of nodes in the top community.
Download: TXT Report CSV Report More Options
Discourse Structure Advice:
N/A
Structural Gap Insight
(topics that could be better linked):N/A
? A structural gap shows the two distinct communities (clusters of words) in this graph that are important, but not yet connected. That's where the new potential and innovative ideas may reside.
This measure is based on a combination of the graph's connectivity and community structure, selecting the groups of nodes that would either make the graph more connected if it's too dispersed or that would help maintain diversity if it's too connected.
This measure is based on a combination of the graph's connectivity and community structure, selecting the groups of nodes that would either make the graph more connected if it's too dispersed or that would help maintain diversity if it's too connected.
Latent Topical Connectors
(less visible terms that link important topics):
N/A
? These are the latent brokers between the topics: the nodes that have an unusually high rate of influence (betweenness centrality) to their freqency — meaning they may appear not as often as the most influential nodes but they are important narrative shifting points.
These are usually brokers between different clusters / communities of nodes, playing not easily noticed and yet important role in this network, like the "grey cardinals" of sorts.
These are usually brokers between different clusters / communities of nodes, playing not easily noticed and yet important role in this network, like the "grey cardinals" of sorts.
Emerging Keywords
N/A
Evolution of Topics
(number of occurrences per text segment) ?
↻
The chart shows how the main topics and the most influential keywords evolved over time. X-axis: time period (split into 10% blocks). Y-axis: cumulative number of occurrences.
Drag the slider to see how the narrative evolved over time. Select the checkbox to recalculate the metrics at every step (slower, but more precise).
Drag the slider to see how the narrative evolved over time. Select the checkbox to recalculate the metrics at every step (slower, but more precise).
Main Topics
(according to Latent Dirichlet Allocation):loading...
⤓ ? ⤓LDA stands for Latent Dirichlet Allocation — it is a topic modelling algorithm based on calculating the maximum probability of the terms' co-occurrence in a particular text or a corpus.
We provide this data for you to be able to estimate the precision of the default InfraNodus topic modeling method based on text network analysis.
We provide this data for you to be able to estimate the precision of the default InfraNodus topic modeling method based on text network analysis.
Most Influential Words
(main topics and words according to LDA):loading...
We provide LDA stats for comparison purposes only. It works with English-language texts at the moment. More languages are coming soon, subscribe @noduslabs to be informed.
Sentiment Analysis
positive: | negative: | neutral:
⤓ ? ⤓
We analyze the sentiment of each statement to see whether it's positive, negative, or neutral. You can filter the statements by sentiment (clicking above) and see what kind of topics correlate with every mood.
The approach is based on AFINN and Emoji Sentiment Ranking
The approach is based on AFINN and Emoji Sentiment Ranking
Use the Bert AI model for English, Dutch, German, French, Spanish and Italian to get more precise results (slower). Standard model is faster, works for English only, is less precise, and is based on a fixed AFINN dictionary.
Keyword Relations Analysis:
please, select the node(s) on the graph see their connections...
+ ?
Top Relations in 4-grams
(bidirectional, for directional bigrams see the CSV table below):
The most prominent relations between the nodes that exist in this graph are shown above. We treat the graph as undirected by default. Occurrences shows the number of the times a relationship appears in a 4-gram window. Weight shows the weight of that relation.
As an option, you can also downloaded directed bigrams above, in case the direction of the relations is important (for any application other than language).
As an option, you can also downloaded directed bigrams above, in case the direction of the relations is important (for any application other than language).
Text Statistics:
| Word Count | Unique Lemmas | Characters | Lemmas Density |
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Text Network Statistics:
The higher is the network's structure diversity and the higher is the alpha in the influence propagation score, the higher is its mind-viral immunity — that is, such network will be more resilient and adaptive than a less diverse one.
In case of a discourse network, high mind-viral immunity means that the text proposes multiple points of view and propagates its influence using both highly influential concepts and smaller, secondary topics.
In case of a discourse network, high mind-viral immunity means that the text proposes multiple points of view and propagates its influence using both highly influential concepts and smaller, secondary topics.
The higher is the diversity, the more distinct communities (topics) there are in this network, the more likely it will be pluralist.
The network structure indicates the level of its diversity. It is based on the modularity measure (>0.4 for medium, >0.65 for high modularity, measured with Louvain (Blondel et al 2008) community detection algorithm) in combination with the measure of influence distribution (the entropy of the top nodes' distribution among the top clusters), as well as the the percentage of nodes in the top community.
| Modularity | 0 |
Influence Distribution | 0 % |
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| Topics | Nodes in Top Topic | Components | Nodes in Top Comp |
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| Nodes | Av Degree | Density | Weighed Betweenness |
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Narrative Influence Propagation:
? The chart above shows how influence propagates through the network. X-axis: lemma to lemma step (narrative chronology). Y-axis: change of influence.
The more even and rhythmical this propagation is, the stronger is the central idea or agenda (see alpha exponent below ~ 0.5 or less).
The more variability can be seen in the propagation profile, the less is the reliance on the main concepts (agenda), the stronger is the role of secondary topical clusters in the narrative.
The more even and rhythmical this propagation is, the stronger is the central idea or agenda (see alpha exponent below ~ 0.5 or less).
The more variability can be seen in the propagation profile, the less is the reliance on the main concepts (agenda), the stronger is the role of secondary topical clusters in the narrative.
We plot the narrative as a time series of influence (using the words' betweenness score). We then apply detrended fluctuation analysis to identify fractality of this time series, plotting the log2 scales (x) to the log2 of accumulated fluctuations (y). If the resulting loglog relation can be approximated on a linear polyfit, there may be a power-law relation in how the influence propagates in this narrative over time (e.g. most of the time non-influential words, occasionally words with a high influence).
Using the alpha exponent of the fit (which is closely related to Hurst exponent)), we can better understand the nature of this relation: uniform (pulsating | alpha <= 0.65), variable (stationary, has long-term correlations | 0.65 < alpha <= 0.85), fractal (adaptive | 0.85 < alpha < 1.15), and complex (non-stationary | alpha >= 1.15).
For maximal diversity, adaptivity, and plurality, the narrative should be close to "fractal" (near-critical state). For fiction, essays, and some forms of poetry — "uniform". Informative texts will often have "variable + stationary" score. The "complex" state is an indicator that the text is always shifting its state.
Using the alpha exponent of the fit (which is closely related to Hurst exponent)), we can better understand the nature of this relation: uniform (pulsating | alpha <= 0.65), variable (stationary, has long-term correlations | 0.65 < alpha <= 0.85), fractal (adaptive | 0.85 < alpha < 1.15), and complex (non-stationary | alpha >= 1.15).
For maximal diversity, adaptivity, and plurality, the narrative should be close to "fractal" (near-critical state). For fiction, essays, and some forms of poetry — "uniform". Informative texts will often have "variable + stationary" score. The "complex" state is an indicator that the text is always shifting its state.
Degree Distribution:
? (based on kolmogorov-smirnov test) ? switch to linear
Using this information, you can identify whether the network has scale-free / small-world (long-tail power law distribution) or random (normal, bell-shaped distribution) network properties.
This may be important for understanding the level of resilience and the dynamics of propagation in this network. E.g. scale-free networks with long degree tails are more resilient against random attacks and will propagate information across the whole structure better.
This may be important for understanding the level of resilience and the dynamics of propagation in this network. E.g. scale-free networks with long degree tails are more resilient against random attacks and will propagate information across the whole structure better.
If a power-law is identified, the nodes have preferential attachment (e.g. 20% of nodes tend to get 80% of connections), and the network may be scale-free, which may indicate that it's more resilient and adaptive. Absence of power law may indicate a more equalized distribution of influence.
Kolmogorov-Smirnov test compares the distribution above to the "ideal" power-law ones (^1, ^1.5, ^2) and looks for the best fit. If the value d is below the critical value cr it is a sign that the both distributions are similar.
Kolmogorov-Smirnov test compares the distribution above to the "ideal" power-law ones (^1, ^1.5, ^2) and looks for the best fit. If the value d is below the critical value cr it is a sign that the both distributions are similar.