**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Publication# Physical realizability of small-world networks

Abstract

Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost associated with their length l, the corresponding distribution q(l) plays a crucial role. Uniform length distributions have received the most attention despite indications that q(l)similar to l(-alpha) exists-e.g., for integrated circuits, the Internet, and cortical networks. While length distributions of this type were previously examined in the context of navigability, we here discuss for such systems the emergence and physical realizability of small-world topology. Our simple argument allows us to understand under which condition and at what expense a small world results.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related MOOCs (32)

Related publications (61)

Related concepts (38)

Advanced statistical physics

We explore statistical physics in both classical and open quantum systems. Additionally, we will cover probabilistic data analysis that is extremely useful in many applications.

Advanced statistical physics

We explore statistical physics in both classical and open quantum systems. Additionally, we will cover probabilistic data analysis that is extremely useful in many applications.

Selected Topics on Discrete Choice

Discrete choice models are used extensively in many disciplines where it is important to predict human behavior at a disaggregate level. This course is a follow up of the online course “Introduction t

Ontological neighbourhood

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

Continuous uniform distribution

In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, and which are the minimum and maximum values. The interval can either be closed (i.e. ) or open (i.e. ). Therefore, the distribution is often abbreviated where stands for uniform distribution.

Exponential distribution

In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.

Recently, there have been multiple proposals for faster methods to calculate glare metrics, daylight glare probability (DGP) in particular. This is driven simultaneously by the lengthy times required to simulate DGP with a conventional image-based approach ...

2022Interactions are ubiquitous in our world, spanning from social interactions between human individuals to physical interactions between robots and objects to mechanistic interactions among different components of an intelligent system. Despite their prevale ...

Humans can rapidly estimate the statistical properties of groups of stimuli, including their average and variability. But recent studies of so-called Feature Distribution Learning (FDL) have shown that observers can quickly learn even more complex aspects ...