What is the maximum number of neighbors k that is possible in Watts and Strogatz regular graph model with N nodes?
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What is the maximum number of neighbors k that is possible in Watts and Strogatz regular graph model with N nodes?
In conclusion, it is found that, regardless of the group size and rewiring probability, 2 to 18 neighbors can help the economic system reach the highest utility growth rate. Furthermore, given the range of neighbors and group size of a Watts-Strogatz model based system, the range of its edges can be calculated too.
What are the key properties of networks generated by a Watts strogatz model?
The three properties of interest are the average path length, the clustering coefficient, and the degree distribution.
What can NetworkX do?
NetworkX provides classes for graphs which allow multiple edges between any pair of nodes. The MultiGraph and MultiDiGraph classes allow you to add the same edge twice, possibly with different edge data. This can be powerful for some applications, but many algorithms are not well defined on such graphs.
How do you make a watt strogatz model?
Creating a Watts-Strogatz graph has two basic steps:
- Create a ring lattice with. nodes of mean degree. . Each node is connected to its. nearest neighbors on either side.
- For each edge in the graph, rewire the target node with probability. . The rewired edge cannot be a duplicate or self-loop.
What is a high clustering coefficient?
Specifically, the clustering coefficient is a measure of the density of the 1.5-degree egocentric network for each vertex. When these connections are dense, the clustering coefficient is high. If your “friends” (alters) all know each other, you have a high clustering coefficient.
How do you know if a graph is a small world?
A graph’s diameter is the maximum of the geodesic distances between node pairs, and the world encapsulated by a graph is “small” if the expected number of hops between two randomly chosen people is small in some sense.
When should I use NetworkX?
NetworkX is a Python language software package for the creation, manipulation, and study of the structure, dynamics, and function of complex networks. It is used to study large complex networks represented in form of graphs with nodes and edges. Using networkx we can load and store complex networks.
What is the small world effect?
The “small-world effect” is the observation that one can find a short chain of acquaintances, often of no more than a handful of individuals, connecting almost any two people on the planet.
Is Erdos Renyi small world?
Erdös-Rényi random networks (ER random networks) do have a low average path length, meaning that there tends to be a path between a pair of nodes that involves only a few edges. This property is shared by many real world networks, and is often called the small world property.
What does a higher clustering coefficient of a graph represent?
This indicates that for a given degree distribution, the clustering leads to a larger percolation threshold, mainly because for a fixed number of links, the clustering structure reinforces the core of the network with the price of diluting the global connections.
How do you interpret clustering coefficients?
Clustering coefficient is a property of a node in a network. Roughly speaking it tells how well connected the neighborhood of the node is. If the neighborhood is fully connected, the clustering coefficient is 1 and a value close to 0 means that there are hardly any connections in the neighborhood.
How do you tell if a network is a small-world network?
In particular, a network is said to be a small-world network (or to satisfy the small-world property) if the mean geodesic distance between pairs of nodes is small relative to the total number of nodes in the network—usually, one wants this length \ell to grow no faster than logarithmically as the number of nodes tends …
How do you calculate a small-world?
The small-world quotient is obtained by dividing the ratio of observed and expected average local clustering coefficient of a network by the ratio of its observed and expected average path length.
How many nodes can NetworkX handle?
For NetworkX, a graph with more than 100K nodes may be too large. I’ll demonstrate that it can handle a network with 187K nodes in this post, but the centrality calculations were prolonged. Luckily, there are some other packages available to help us with even larger graphs.
How do you know if a graph is a small-world?
How do I know if my network is a small-world?
Small-world networks should have some spatial structure, which is reflected by a high clustering coefficient. By contrast, random networks have no such structure and a low clustering coefficient.
What is the smallest network in the world?
1. Personal Area Network (PAN) The smallest and most basic type of network, a PAN is made up of a wireless modem, a computer or two, phones, printers, tablets, etc., and revolves around one person in one building.
What is clustering coefficient Networkx?
The local clustering coefficient of the green node is computed as the proportion of connections among its neighbours. Here is the code to implement the above clustering coefficient in a graph. It is a part of the networkx library and can be directly accessed using it.
