Small World

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A useful method to analyze network robustness is the percolation theory. The main mechanism to construct small-world networks is the Watts—Strogatz mechanism. Small-world networks can also be introduced with time-delay, [19] which will not only produce fractals but also chaos [20] under the right conditions, or transition to chaos in dynamics networks.

Degree—diameter graphs are constructed such that the number of neighbors each vertex in the network has is bounded, while the distance from any given vertex in the network to any other vertex the diameter of the network is minimized. Constructing such small-world networks is done as part of the effort to find graphs of order close to the Moore bound. Another way to construct a small world network from scratch is given in Barmpoutis et al. A fast algorithm of constant complexity is given, along with measurements of the robustness of the resulting graphs.

Depending on the application of each network, one can start with one such "ultra small-world" network, and then rewire some edges, or use several small such networks as subgraphs to a larger graph. Small-world properties can arise naturally in social networks and other real-world systems via the process of dual-phase evolution.

This is particularly common where time or spatial constraints limit the addition of connections between vertices The mechanism generally involves periodic shifts between phases, with connections being added during a "global" phase and being reinforced or removed during a "local" phase. Diffusion-limited aggregation , Pattern formation. The advantages to small world networking for social movement groups are their resistance to change due to the filtering apparatus of using highly connected nodes, and its better effectiveness in relaying information while keeping the number of links required to connect a network to a minimum.

The small world network model is directly applicable to affinity group theory represented in sociological arguments by William Finnegan. Affinity groups are social movement groups that are small and semi-independent pledged to a larger goal or function. Though largely unaffiliated at the node level, a few members of high connectivity function as connectivity nodes, linking the different groups through networking. This small world model has proven an extremely effective protest organization tactic against police action.

A practical example of this is small world networking through affinity groups that William Finnegan outlines in reference to the Seattle WTO protests. Many networks studied in geology and geophysics have been shown to have characteristics of small-world networks. Networks defined in fracture systems and porous substances have demonstrated these characteristics.

Climate networks may be regarded as small world networks where the links are of different length scales. Small-world networks have been used to estimate the usability of information stored in large databases. This usability typically comes at the cost of the amount of information that can be stored in the same repository.

The Freenet peer-to-peer network has been shown to form a small-world network in simulation, [30] allowing information to be stored and retrieved in a manner that scales efficiency as the network grows. Both anatomical connections in the brain [31] and the synchronization networks of cortical neurons [32] exhibit small-world topology.

A small-world network of neurons can exhibit short-term memory. A computer model developed by Solla et al. An activating pulse generated self-sustaining loops of communication activity among the neurons. A second pulse ended this activity.

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The pulses switched the system between stable states: Small world neuronal networks have also been used as models to understand seizures. On a more general level, many large-scale neural networks in the brain, such as the visual system and brain stem, exhibit small-world properties.

The WS model includes a uniform distribution of long-range links. When the distribution of link lengths follows a power law distribution, the mean distance between two sites changes depending on the power of the distribution. From Wikipedia, the free encyclopedia. Evidence for a crossover picture". B , —, doi: Comparing indices of small worldliness". Havlin , and D.

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Handbook of graphs and networks. American Physical Society 3. Current Opinion in Structural Biology. Assuming an age difference of 70 years between any two connected people in the chain that connects the two, this would necessitate at least 32 connections between Einstein and Alexander the Great. Yang, Chaos in small-world networks, Phys. Yang, Small-world networks in geophysics, Geophys. Posadas, Small-world in a seismic network: Small world networks key to memory.

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Small-world network

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