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**clustering small world networks**
1

A small-world network is a type of mathematical graph in which most nodes are not neighbors ... while the global clustering coefficient is not small.

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**Small-world network - Wikipedia***https://en.wikipedia.org/wiki/Small-world_network*A small-world network is a type of mathematical graph in which most nodes are not neighbors ... while the global clustering coefficient is not small.

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2

The Watts and Strogatz model (WS model) accounts for clustering while retaining the short average path lengths of the ER model. • The WS model interpolates ...

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**Small World Networks - Jackson State University***https://www.jsums.edu/nmeghanathan/files/2015/08/CSC641-Fall2015-Module-6-Small-World-Networks-reduced.pdf*The Watts and Strogatz model (WS model) accounts for clustering while retaining the short average path lengths of the ER model. • The WS model interpolates ...

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3

The current accepted definition of a small-world network is that it has clustering similar to a regular lattice and path length similar to a random network.

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**The Ubiquity of Small-World Networks - PMC - NCBI***https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3604768/*The current accepted definition of a small-world network is that it has clustering similar to a regular lattice and path length similar to a random network.

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4

Summary · Small-world networks are designed to generate networks that are similar to real-world networks to provide a mathematical explanation of ...

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**What are Small-world Network Models? | by Yi-Tang Wang***https://towardsdatascience.com/what-are-small-world-network-models-87bbcfe0e038*Summary · Small-world networks are designed to generate networks that are similar to real-world networks to provide a mathematical explanation of ...

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5

In mathematics and social psychology, a small-world network is a class of random graphs where most nodes are not neighbors of one another, but most nodes ...

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**Small-world networks | Psychology Wiki - Fandom***https://psychology.fandom.com/wiki/Small-world_networks*In mathematics and social psychology, a small-world network is a class of random graphs where most nodes are not neighbors of one another, but most nodes ...

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6

Milgram's small world experiment. □ Local structure. □ clustering coefficient. □ motifs. □ Small world network models: □ Watts & Strogatz (clustering ...

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**Small world networks - SNAP: Stanford***http://snap.stanford.edu/class/cs224w-2015/slides/05-smallworlds.pdf*Milgram's small world experiment. □ Local structure. □ clustering coefficient. □ motifs. □ Small world network models: □ Watts & Strogatz (clustering ...

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7

Networks with short average path lengths and high clustering coefficients are considered small world networks. See the Statistics section of HOW TO USE IT ...

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**Small Worlds - NetLogo Models Library***https://ccl.northwestern.edu/netlogo/models/SmallWorlds*Networks with short average path lengths and high clustering coefficients are considered small world networks. See the Statistics section of HOW TO USE IT ...

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8

We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We ...

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**Collective dynamics of 'small-world' networks - Nature***https://www.nature.com/articles/30918*We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We ...

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9

Small world networks and clustered small world networks with random connectivity. Social Network Analysis and Mining, Springer, 2012.

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**Small world networks and clustered ... - Archive ouverte HAL***https://hal.archives-ouvertes.fr/hal-00679660/document*Small world networks and clustered small world networks with random connectivity. Social Network Analysis and Mining, Springer, 2012.

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10

The small characteristic path length in small-world networks points to the importance of short paths between any two vertices. In the case of biological ...

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**Small-World Property | SpringerLink***https://link.springer.com/10.1007/978-1-4419-9863-7_2*The small characteristic path length in small-world networks points to the importance of short paths between any two vertices. In the case of biological ...

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11

Abstract. Small-worlds represent efficient communication networks that obey two distinguishing characteristics: a high clustering coefficient together with ...

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**Small-Worlds: Strong Clustering in Wireless Networks - arXiv***https://arxiv.org/pdf/0706.1063*Abstract. Small-worlds represent efficient communication networks that obey two distinguishing characteristics: a high clustering coefficient together with ...

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12

Small world phenomenon. ▫ Milgram's small world experiment. ▫ Small world network models: ▫ Watts & Strogatz (clustering & short paths).

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**Small World Networks - Computer Science***https://cs.brynmawr.edu/Courses/cs380/spring2013/section02/slides/06_SmallWorldNetworks.pdf*Small world phenomenon. ▫ Milgram's small world experiment. ▫ Small world network models: ▫ Watts & Strogatz (clustering & short paths).

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13

Clustering in Small-World Networks ... Clustering can be used to quantify network robustness with respect to perturbation, and a high degree of clustering is one ...

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**Clustering in Small-World Networks: New in Mathematica 9***https://www.wolfram.com/mathematica/new-in-9/social-network-analysis/clustering-in-small-world-networks.html*Clustering in Small-World Networks ... Clustering can be used to quantify network robustness with respect to perturbation, and a high degree of clustering is one ...

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14

In a graph with a "small world" topology, nodes are highly clustered yet the path length between them is small. Small world networks which have already been ...

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**The Small World Web - HP Labs***https://www.hpl.hp.com/research/idl/papers/smallworld/smallworldpaper.html*In a graph with a "small world" topology, nodes are highly clustered yet the path length between them is small. Small world networks which have already been ...

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15

A key concept in defining small-worlds networks is that of 'clustering' which measures the extent to which the neighbors of a node are also ...

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**Network 'Small-World-Ness': A Quantitative Method for ... - PLOS***https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0002051*A key concept in defining small-worlds networks is that of 'clustering' which measures the extent to which the neighbors of a node are also ...

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16

Many networks in the real world, including social networks, have the “small world property”, which is that the average distance between nodes, ...

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**Chapter 3 Small World Graphs - Green Tea Press***https://greenteapress.com/complexity2/html/thinkcomplexity2004.html*Many networks in the real world, including social networks, have the “small world property”, which is that the average distance between nodes, ...

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17

can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them. 'small-world' networks, by ...

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**Collective Dynamics of Small-World Networks***http://worrydream.com/refs/Watts-CollectiveDynamicsOfSmallWorldNetworks.pdf*can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them. 'small-world' networks, by ...

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18

The clustering coefficient C is defined as the average over all vertices of the fraction of the number of connected pairs of neighbors for each vertex, ...

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**Topology of small-world networks of protein–protein complex ...***https://academic.oup.com/bioinformatics/article/21/8/1311/249420*The clustering coefficient C is defined as the average over all vertices of the fraction of the number of connected pairs of neighbors for each vertex, ...

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19

Abstract: Small-world networks are a very commonly occurring type of graph in the real-world, which exhibit a clustered structure that is not well ...

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**Node-attribute Graph Layout for Small-World Networks***https://ieeexplore.ieee.org/document/6004088*Abstract: Small-world networks are a very commonly occurring type of graph in the real-world, which exhibit a clustered structure that is not well ...

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20

Keywords: Networks, clusters, small worlds, organization design, new organizational forms. In recent years, many industries have seen a rise in business ...

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**NETWORKS, CLUSTERS, AND SMALL WORLDS***https://www.jorgdesign.net/article/download/20478/18727/48415*Keywords: Networks, clusters, small worlds, organization design, new organizational forms. In recent years, many industries have seen a rise in business ...

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21

Small-world networks should have some spatial structure, which is reflected by a high clustering coefficient. By contrast, random networks ...

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**How to test statistically whether my network (graph) is a "small ...***https://stats.stackexchange.com/questions/175492/how-to-test-statistically-whether-my-network-graph-is-a-small-world-network*Small-world networks should have some spatial structure, which is reflected by a high clustering coefficient. By contrast, random networks ...

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22

Watts and Strogatz demonstrated a small world model that can generate a network that has short paths and is highly clustered. This model starts with a regular ...

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**Small World Networks - FutureLearn***https://www.futurelearn.com/info/courses/social-media/0/steps/16045*Watts and Strogatz demonstrated a small world model that can generate a network that has short paths and is highly clustered. This model starts with a regular ...

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23

CS 4884: Erdös-Renyi and Small World Networks. T. M. Murali ... highly clustered, like regular lattices, yet have small characteristic.

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**CS 4884: Erdös-Renyi and Small World Networks***http://bioinformatics.cs.vt.edu/~murali/teaching/2020-spring-cs4884/lectures/lecture-05-small-world-networks.pdf*CS 4884: Erdös-Renyi and Small World Networks. T. M. Murali ... highly clustered, like regular lattices, yet have small characteristic.

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24

At the same time, the average connectivity increases as a power of the network size, while the average clustering coefficients and average path ...

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**(PDF) Small-World Properties of Facebook Group Networks***https://www.researchgate.net/publication/289259407_Small-World_Properties_of_Facebook_Group_Networks*At the same time, the average connectivity increases as a power of the network size, while the average clustering coefficients and average path ...

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25

Small world models are networks consisting of many local links and fewer long range `shortcuts', used to model networks with a high degree of local ...

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**Discrete small world networks - Project Euclid***https://projecteuclid.org/journals/electronic-journal-of-probability/volume-11/issue-none/Discrete-small-world-networks/10.1214/EJP.v11-381.full*Small world models are networks consisting of many local links and fewer long range `shortcuts', used to model networks with a high degree of local ...

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26

A small world network is characterized by a small average shortest path length, and a large clustering coefficient. Small-worldness is commonly measured ...

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**Small-world — NetworkX 2.8.8 documentation***https://networkx.org/documentation/stable/reference/algorithms/smallworld.html*A small world network is characterized by a small average shortest path length, and a large clustering coefficient. Small-worldness is commonly measured ...

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27

Small World Networks · Regular network: rewiring probability of 0.0, average clustering coefficient of 0.50, average path length of 12.88 · Small world network: ...

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**Small World Networks - Medium***https://medium.com/@HugoAContrerasP/small-world-networks-2faa5323a77e*Small World Networks · Regular network: rewiring probability of 0.0, average clustering coefficient of 0.50, average path length of 12.88 · Small world network: ...

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28

Watts and Strogatz came up with a model about how to construct Small World Networks. Let there be n nodes, where each node is connected to m ...

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**Small World Model - Using Python Networkx - GeeksforGeeks***https://www.geeksforgeeks.org/small-world-model-using-python-networkx/*Watts and Strogatz came up with a model about how to construct Small World Networks. Let there be n nodes, where each node is connected to m ...

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29

The lattice is converted to a small-world network (B) by the algorithm of ... In particular, a high level of clustering has been observed in ...

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**Methods for Generating Complex Networks with Selected ...***https://www.frontiersin.org/articles/10.3389/fncom.2011.00011/full*The lattice is converted to a small-world network (B) by the algorithm of ... In particular, a high level of clustering has been observed in ...

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30

An increase of the "rewiring probability" p (the probability that an edge is disconnected from one of its nodes and then randomly connected to another ...

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**Small world network regime - MathOverflow***https://mathoverflow.net/questions/383841/small-world-network-regime*An increase of the "rewiring probability" p (the probability that an edge is disconnected from one of its nodes and then randomly connected to another ...

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31

high clustering and short path length; and about 10 years since this metric of ... graph theory, small-world network, network neuroscience, connectomics, ...

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**Small-World Brain Networks Revisited - SAGE Journals***https://journals.sagepub.com/doi/pdf/10.1177/1073858416667720*high clustering and short path length; and about 10 years since this metric of ... graph theory, small-world network, network neuroscience, connectomics, ...

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32

Netlogo simulation on small worlds starts with a high clustering coefficient and with a very small average path length. So basically just like ...

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**Small World Networks - Network Evolution | Coursera***https://www.coursera.org/lecture/social-network-analysis/small-world-networks-0pCGr*Netlogo simulation on small worlds starts with a high clustering coefficient and with a very small average path length. So basically just like ...

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33

This example shows how to construct and analyze a Watts-Strogatz small-world graph. The Watts-Strogatz model is a random graph that has small-world network ...

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**Build Watts-Strogatz Small World Graph Model - MathWorks***https://www.mathworks.com/help/matlab/math/build-watts-strogatz-small-world-graph-model.html*This example shows how to construct and analyze a Watts-Strogatz small-world graph. The Watts-Strogatz model is a random graph that has small-world network ...

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34

In addition to this, social networks also have a large clustering coefficient, i.e. they contain a large number of triangles. As an example of a social network, ...

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**Small-World Networks (Chapter 4) - Cambridge University Press***https://www.cambridge.org/core/books/complex-networks/smallworld-networks/CA3287F880ABDFA3CAEB49164CA829B7*In addition to this, social networks also have a large clustering coefficient, i.e. they contain a large number of triangles. As an example of a social network, ...

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35

These community structures are densely connected regions of nodes in a network that are loosely connected to each other. The model generates these clustered ...

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**Small world networks and clustered small world networks with ...***https://hal.inria.fr/hal-00679660*These community structures are densely connected regions of nodes in a network that are loosely connected to each other. The model generates these clustered ...

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36

In the vast realm of spatial network models, only a few repro- duce even the most basic properties of real-world networks. Here, we focus on ...

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**Small worlds and clustering in spatial networks***https://link.aps.org/pdf/10.1103/PhysRevResearch.2.023040*In the vast realm of spatial network models, only a few repro- duce even the most basic properties of real-world networks. Here, we focus on ...

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37

Figure 20.2: The Watts-Strogatz model arises from a highly clustered network (such as the grid), with a small number of random links added in. and 20.1(b).

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**Chapter 20 The Small-World Phenomenon - Cornell CS***https://www.cs.cornell.edu/home/kleinber/networks-book/networks-book-ch20.pdf*Figure 20.2: The Watts-Strogatz model arises from a highly clustered network (such as the grid), with a small number of random links added in. and 20.1(b).

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38

In order to model the real-world networks, graphs must have both clustering and small- world properties. Random graphs show the small-world effect – average ...

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**Models of the Small World - Department of Theoretical Physics***http://www-f1.ijs.si/~rudi/sola/prizmic.pdf*In order to model the real-world networks, graphs must have both clustering and small- world properties. Random graphs show the small-world effect – average ...

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39

Table A2.1: Calculating the small-world quotient for local, regional, and multi-level networks. Network. Observed average local clustering coefficient.

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**Appendix 2 Small-world Quotient Calculation Table A2.1***https://www.ecologyandsociety.org/vol23/iss2/art48/appendix2.pdf*Table A2.1: Calculating the small-world quotient for local, regional, and multi-level networks. Network. Observed average local clustering coefficient.

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40

The small-world phenomenon formalized in this article as the coinci- dence of high local clustering and short global separation, is shown.

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**Networks, Dynamics, and the Small-World Phenomenon1 - jstor***https://www.jstor.org/stable/10.1086/210318*The small-world phenomenon formalized in this article as the coinci- dence of high local clustering and short global separation, is shown.

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41

Real-world social networks tend to be small worlds. In a small world, people are clustered in groups, but despite this, are still, on average, socially ...

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**13 Bridges, Holes, the Small World Problem, and Simulation***https://bookdown.org/markhoff/social_network_analysis/bridges-holes-the-small-world-problem-and-simulation.html*Real-world social networks tend to be small worlds. In a small world, people are clustered in groups, but despite this, are still, on average, socially ...

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42

Also given in Table 1.1 are the values Crand that the clustering coefficient would have for random graphs of the same size and coordination number. Note that ...

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**Graph Theory and Small-World Networks***https://itp.uni-frankfurt.de/~gros/Vorlesungen/CADS/CADS-networks.pdf*Also given in Table 1.1 are the values Crand that the clustering coefficient would have for random graphs of the same size and coordination number. Note that ...

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43

Lattice Networks. ○ Small World Networks. ○ Part 3: Properties of Small World Networks ... clusters. ○ Any vertex can be reached by any other vertex.

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**Small World Networks - Semantic Scholar***https://pdfs.semanticscholar.org/d3d6/cc6004bc2f863d4f558d49da4d748cb00e9d.pdf*Lattice Networks. ○ Small World Networks. ○ Part 3: Properties of Small World Networks ... clusters. ○ Any vertex can be reached by any other vertex.

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44

Abstract—Small-world graphs, exhibiting high clustering coefficients and small average path length, have been shown to capture fundamental properties of a ...

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**Network Information Flow in Navigable Small-World Networks***http://www.mit.edu/~medard/costa-barros.pdf*Abstract—Small-world graphs, exhibiting high clustering coefficients and small average path length, have been shown to capture fundamental properties of a ...

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45

Small world networks · Building a taxonomy of static and dynamic properties whose presence or absence in a network can be easily checked.

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**Small world networks | Michael Nielsen***https://michaelnielsen.org/blog/small-world-networks/*Small world networks · Building a taxonomy of static and dynamic properties whose presence or absence in a network can be easily checked.

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46

One of our main results is that for intermediate values of p, the graph is a small-world network: highly clustered like a regular graph, yet with small ...

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**Collective dynamics of 'small-world' networks - Sasank's Blog***https://chsasank.com/classic_papers/collective-dynamics-of-small-world-networks.html*One of our main results is that for intermediate values of p, the graph is a small-world network: highly clustered like a regular graph, yet with small ...

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47

Scale-free networks are also small-world networks, because (i) they have clustering coefficients much larger than random networks (2) and (ii) their ...

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**Classes of small-world networks - PNAS***https://www.pnas.org/doi/full/10.1073/pnas.200327197*Scale-free networks are also small-world networks, because (i) they have clustering coefficients much larger than random networks (2) and (ii) their ...

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48

A small world network's resilience comes from a combination of its cluster which encourages cohesion and the interconnections between the ...

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**Small World Networks Theoretical Framework for the ...***https://upland-resilience.org/small-world-networks-theoretical-framework-for-the-results-project/*A small world network's resilience comes from a combination of its cluster which encourages cohesion and the interconnections between the ...

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49

This paper presents a study of two small-world network models in clustering formation and routing in wireless network, the Watts and Stragtz's (WS) and the ...

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**An Experimental Study of Small World Network Models for ...***https://journals.riverpublishers.com/index.php/JCSANDM/article/download/5169/3771/14751*This paper presents a study of two small-world network models in clustering formation and routing in wireless network, the Watts and Stragtz's (WS) and the ...

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50

Example networks are presented that would be interpreted as small-world when clustering is compared to a random network but are not small-world according to [ ...

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**The Ubiquity of Small-World Networks - ProQuest***https://search.proquest.com/openview/c61cb6e238c4ec1f0633cebf930c7e8f/1?pq-origsite=gscholar&cbl=2029230*Example networks are presented that would be interpreted as small-world when clustering is compared to a random network but are not small-world according to [ ...

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51

We show that Facebook group networks have small average path lengths and large clustering coefficients that do not vanish with increased network size, ...

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**Small-World Properties of Facebook Group Networks***https://digitalcommons.unomaha.edu/mathfacpub/61/*We show that Facebook group networks have small average path lengths and large clustering coefficients that do not vanish with increased network size, ...

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52

A small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely ...

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**Small-world network - English Wikipedia - WikiDeck***https://wikideck.com/Small-world_network*A small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely ...

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53

Small-world networks distinguish themselves from others by their high clustering coefficient and short average path length. In the past dozen years, many ...

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**A Tree-Structured Deterministic Small-World Network - J-Stage***https://www.jstage.jst.go.jp/article/transinf/E95.D/5/E95.D_5_1536/_article/-char/en*Small-world networks distinguish themselves from others by their high clustering coefficient and short average path length. In the past dozen years, many ...

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54

C clustering coefficient: Ci fraction of existing connections between nearest neighbours of node i. C is the average over Ci. Small world effect:.

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**Statistics for Watts-Strogatz Small World Networks***https://www.stats.ox.ac.uk/~reinert/talks/swtalkparis.pdf*C clustering coefficient: Ci fraction of existing connections between nearest neighbours of node i. C is the average over Ci. Small world effect:.

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55

That is, each node is connected to every other node with small degrees of separation, despite the fact that most nodes exist in tight clusters.

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**Small World and Scale-Free Networks***https://dshizuka.github.io/networkanalysis/example1_smallworld.html*That is, each node is connected to every other node with small degrees of separation, despite the fact that most nodes exist in tight clusters.

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56

Watts & Strogatz. Scale-free networks. Clustering Coefficient. Small World Networks. SET07106 Mathematics for Software Engineering. School of Computing.

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**Small World Networks - Uta Priss***https://www.upriss.org.uk/maths/mlec5a.pdf*Watts & Strogatz. Scale-free networks. Clustering Coefficient. Small World Networks. SET07106 Mathematics for Software Engineering. School of Computing.

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57

benmaier / smallworld ... Generate and analyze small-world networks according to the revised Watts-Strogatz model where the randomization at β = 1 is truly equal ...

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**small-world-networks · GitHub Topics***https://github.com/topics/small-world-networks*benmaier / smallworld ... Generate and analyze small-world networks according to the revised Watts-Strogatz model where the randomization at β = 1 is truly equal ...

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58

Small-world networks and scale-free networks are important complex network models with massive number of nodes and have been actively used to study the ...

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**Small-World and Scale-Free Network Models for IoT Systems***https://www.hindawi.com/journals/misy/2017/6752048/*Small-world networks and scale-free networks are important complex network models with massive number of nodes and have been actively used to study the ...

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59

For this kind of network, the average path length tends to 2 and its clustering coefficient tends to 1, as. N → ∞. The star-shaped network model captures the.

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**Complex networks: Small-world, scale-free and beyond***https://www.ee.cityu.edu.hk/~gchen/pdf/CW-CASM03-overview.pdf*For this kind of network, the average path length tends to 2 and its clustering coefficient tends to 1, as. N → ∞. The star-shaped network model captures the.

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60

Networks with short average path lengths and high clustering coefficients are considered small world networks. (Note: The plots for both the clustering ...

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**Small Worlds, by Uri Wilensky (model ID 1596)***https://modelingcommons.org/browse/one_model/1596*Networks with short average path lengths and high clustering coefficients are considered small world networks. (Note: The plots for both the clustering ...

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61

Small World Networks. 23. 2. 3. Basic Graph Theory. 28. 2.3.1. Paths. 31. 2.3.2. Clustering Coefficients. 33. 2.3.3. Measure of Centrality.

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**Rumor propagation on random and small world networks***https://scholarworks.rit.edu/cgi/viewcontent.cgi?article=8899&context=theses*Small World Networks. 23. 2. 3. Basic Graph Theory. 28. 2.3.1. Paths. 31. 2.3.2. Clustering Coefficients. 33. 2.3.3. Measure of Centrality.

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62

The mean path length is 3.7 and the clustering coefficient is 0.6. A WS model with the same number of nodes and edges, and with probability of ...

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**It's a small world, scale-free network after all***http://allendowney.blogspot.com/2016/09/its-small-world-scale-free-network.html*The mean path length is 3.7 and the clustering coefficient is 0.6. A WS model with the same number of nodes and edges, and with probability of ...

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63

I will discuss a class of random spatial networks and show that they have small world-like properties, but the level of clustering is tunable and we can ...

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**Contagion spread in clustered and unclustered small world ...***https://av.tib.eu/en/media/56464*I will discuss a class of random spatial networks and show that they have small world-like properties, but the level of clustering is tunable and we can ...

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64

high clustering and short path length; and about 10 years since this metric of ... graph theory, small-world network, network neuroscience, connectomics, ...

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**Small-World Brain Networks Revisited - CORE***https://core.ac.uk/download/pdf/77415134.pdf*high clustering and short path length; and about 10 years since this metric of ... graph theory, small-world network, network neuroscience, connectomics, ...

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65

It is also well known that a small-world network displays a stronger synchronizability due to its small average shortest path length, and the type of its ...

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**Robustness of cluster synchronous patterns in small-world ...***https://aip.scitation.org/doi/10.1063/1.4873524*It is also well known that a small-world network displays a stronger synchronizability due to its small average shortest path length, and the type of its ...

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66

However, echoing the Watts-Strogatz procedure, the network construction method employed here includes a probabilistic rewiring phase to establish inter-cluster ...

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**Dynamical Complexity in Small-World Networks of Spiking ...***https://www.doc.ic.ac.uk/~mpsha/ShanahanPhysRevEPreprint.pdf*However, echoing the Watts-Strogatz procedure, the network construction method employed here includes a probabilistic rewiring phase to establish inter-cluster ...

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67

Navigation in Small-Worlds (Kleinberg's ... Random networks tend not to be clustered ... The local clustering coefficient C(v) of vertex v is a.

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**Navigable Small-World Networks - KTH***https://www.kth.se/social/upload/514c7450f276547cb33a1992/2-kleinberg.pdf*Navigation in Small-Worlds (Kleinberg's ... Random networks tend not to be clustered ... The local clustering coefficient C(v) of vertex v is a.

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68

Such networks are called Small world networks. they have the feature of having relative high clustering coefficients but low average path length.

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**Network basics 2 - Systems sciences at ISIS***http://systems-sciences.uni-graz.at/etextbook/networks/networks_2.html*Such networks are called Small world networks. they have the feature of having relative high clustering coefficients but low average path length.

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69

SW networks are very close structurally to many social networks in that they have a higher clustering and almost the same average path than the ...

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**Types of Networks: Random, Small-World, Scale-Free***https://noduslabs.com/radar/types-networks-random-small-world-scale-free/*SW networks are very close structurally to many social networks in that they have a higher clustering and almost the same average path than the ...

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70

Key Points. FRCs form highly clustered network structures.Because of this clustering, FRC networks resemble the famous small-world networks.

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**Local Attachment Explains Small World–like Properties of ...***https://journals.aai.org/jimmunol/article/202/11/3318/107017/Local-Attachment-Explains-Small-World-like*Key Points. FRCs form highly clustered network structures.Because of this clustering, FRC networks resemble the famous small-world networks.

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71

Small world networks are networks with high values of clustering coefficient of the nodes of the networks and very short paths between them ...

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**Relating the small world coefficient to the entropy of 2D ...***https://iopscience.iop.org/article/10.1088/2399-6528/ab41e2/pdf*Small world networks are networks with high values of clustering coefficient of the nodes of the networks and very short paths between them ...

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72

short path-length and clustering means that, in a small-world network, individuals are—on average—a short distance from everyone else in the network, ...

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**Efficiency variation and classification of small-world networks***https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=6084&context=lkcsb_research*short path-length and clustering means that, in a small-world network, individuals are—on average—a short distance from everyone else in the network, ...

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73

... biological, social and information networks fall into the broad class of 'small-world' networks: they how tightly interconnected clusters of nodes, ...

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**Network 'small-world-ness': A quantitative method ... - Mendeley***https://www.mendeley.com/catalogue/c8bc433d-78e8-3fd5-8e33-f2153b8de26b/*... biological, social and information networks fall into the broad class of 'small-world' networks: they how tightly interconnected clusters of nodes, ...

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74

From [Wabs and Strogatz, 1998]. • Characteriscc path length and clustering coefficient for some real networks and for random networks with same number of nodes.

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**Small World and Weak Ties***https://www.cl.cam.ac.uk/teaching/1415/L109/l109-lecture2.pdf*From [Wabs and Strogatz, 1998]. • Characteriscc path length and clustering coefficient for some real networks and for random networks with same number of nodes.

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75

Additional Keywords: Small world networks, multiscale graphs, clustering metric, semantic zooming. 1. SMALL WORLD NETWORKS. The small world phenomenon was ...

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**Multiscale Visualization of Small World Networks***https://webpages.charlotte.edu/krs/courses/6010/infovis/pubs/graphs/auber-infovis03.pdf*Additional Keywords: Small world networks, multiscale graphs, clustering metric, semantic zooming. 1. SMALL WORLD NETWORKS. The small world phenomenon was ...

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76

Abstract—Small-world networks have characteristically low pairwise shortest-path distances, causing distance-based layout methods.

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**Adaptive Disentanglement based on Local Clustering in Small ...***https://d-nb.info/1136271805/34*Abstract—Small-world networks have characteristically low pairwise shortest-path distances, causing distance-based layout methods.

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77

of social, biological, and technological systems [13,14]. Small-world networks exhibit a high degree of clustering and a small average path ...

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**Low-Rank Network Decomposition Reveals Structural ... - Works***https://works.swarthmore.edu/cgi/viewcontent.cgi?article=1164&context=fac-math-stat*of social, biological, and technological systems [13,14]. Small-world networks exhibit a high degree of clustering and a small average path ...

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78

In other words, small-world networks are sparse, highly clustered graphs with small average path length. Small-world networks represent the small-world ...

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**Random Graph Models***https://homepage.cs.uiowa.edu/~sriram/21/spring07/project1.html*In other words, small-world networks are sparse, highly clustered graphs with small average path length. Small-world networks represent the small-world ...

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79

Networks, Dynamics, and the Small-World Phenomenon. Duncan J. Watts ... dence of high local clustering and short global separation, is shown.

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**Networks, dynamics, and the small-world phenomenon***http://www.columbia.edu/itc/sociology/watts/w3233/client_edit/watts_networks.pdf*Networks, Dynamics, and the Small-World Phenomenon. Duncan J. Watts ... dence of high local clustering and short global separation, is shown.

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80

Table: (Excerpt of Table 1 in Newman 2000) The clustering coefficients. C for three real-world networks and the value for C in a random ...

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**M.E.J. Newman: Models of the Small World - Cis Hut Fi***http://www.cis.hut.fi/Opinnot/T-61.184/s07/lecture7.pdf*Table: (Excerpt of Table 1 in Newman 2000) The clustering coefficients. C for three real-world networks and the value for C in a random ...

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81

By using this simple measure, small-world networks are seen as systems that ... acteristic path length L and the clustering coefficient C.

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**Efficient Behavior of Small-World Networks***http://www.maths.qmul.ac.uk/~latora/efficiency_prl_PRL87.pdf*By using this simple measure, small-world networks are seen as systems that ... acteristic path length L and the clustering coefficient C.

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82

Lecture 25, and the small-world P2P networks to be presented ... total number of nodes in the graph, but clustering to remain.

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**Lecture 26: Small-World Peer-to-Peer Networks and Their ...***https://engineering.purdue.edu/kak/compsec/NewLectures/Lecture26.pdf*Lecture 25, and the small-world P2P networks to be presented ... total number of nodes in the graph, but clustering to remain.

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83

The Evolution of a Random Network · Section 3.7. Real Networks are Supercritical · Section 3.8. Small Worlds · Section 3.9. Clustering Coefficient · Section ...

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**Chapter 3 - Network Science by Albert-László Barabási***http://networksciencebook.com/chapter/3*The Evolution of a Random Network · Section 3.7. Real Networks are Supercritical · Section 3.8. Small Worlds · Section 3.9. Clustering Coefficient · Section ...

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84

4.2 Reciprocity. 19. 4.3 Clustering. 19. 4.4 Small World Properties. 20. 4.5 How Graph Theory has Shaped Instagram Applications.

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**Experimental Analysis of Networks in the Age of Social Media***https://fisher.wharton.upenn.edu/wp-content/uploads/2020/09/Thesis_Katherine-Li.pdf*4.2 Reciprocity. 19. 4.3 Clustering. 19. 4.4 Small World Properties. 20. 4.5 How Graph Theory has Shaped Instagram Applications.

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85

Given a network, the small-world effect is simple to measure: one just finds ... Measuring clustering is a little more complicated. Watts and Strogatz.

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**chapter 4: models of networks - De Gruyter***https://www.degruyter.com/document/doi/10.1515/9781400841356.286/pdf*Given a network, the small-world effect is simple to measure: one just finds ... Measuring clustering is a little more complicated. Watts and Strogatz.

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86

I'd now like to generate small world networks with a specified clustering coefficient. I'm new to igraph and this seems like a functionality ...

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**Randomly generate network with specified clustering coefficient***https://stackoverflow.com/questions/60946344/randomly-generate-network-with-specified-clustering-coefficient*I'd now like to generate small world networks with a specified clustering coefficient. I'm new to igraph and this seems like a functionality ...

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87

Clustering in real networks ... clustering coefficient independent of the network size ... The small-world model (Watts and Strogatz 1998) tries to.

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**Part 8: Small-World Network Model - University of Pittsburgh***https://sites.pitt.edu/~kpele/Materials15/module8.pdf*Clustering in real networks ... clustering coefficient independent of the network size ... The small-world model (Watts and Strogatz 1998) tries to.

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88

Many social networks have the following properties: (i) a short average distance between any two individuals; (ii) a high clustering ...

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**Small World Networks with Segregation Patterns and Brokers***https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1443782*Many social networks have the following properties: (i) a short average distance between any two individuals; (ii) a high clustering ...

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89

Small World Networks: Intuition. The Cavemen World: highly clustered social connections. Denis Helic (ISDS, TU Graz). Small-World.

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**Small World Problem - Computational Social Systems 1 (VU ...***https://courses.isds.tugraz.at/dhelic/websci/slides_2020/smallworld.pdf*Small World Networks: Intuition. The Cavemen World: highly clustered social connections. Denis Helic (ISDS, TU Graz). Small-World.

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90

High clustering supports specialization as local collections of strongly interconnected nodes readily share information or resources.

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**The Ubiquity of Small-World Networks | Brain Connectivity***https://www.liebertpub.com/doi/10.1089/brain.2011.0038*High clustering supports specialization as local collections of strongly interconnected nodes readily share information or resources.

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91

Short overall path lengths and high clustering are the characteristic signatures of small world networks. These characteristics result in a graph that is ...

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**Social Networks -- Patterns In Nature, an online book***http://www.patternsinnature.org/Book/SocialNetworks.html*Short overall path lengths and high clustering are the characteristic signatures of small world networks. These characteristics result in a graph that is ...

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92

small-world network structures, and ultimately to provide novel systematic ... scale-free networks with very small clustering and short path.

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**On the effect of the path length of small-world networks on ...***https://www.tandfonline.com/doi/pdf/10.4161/viru.19131*small-world network structures, and ultimately to provide novel systematic ... scale-free networks with very small clustering and short path.

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