31 Jan 2000 | Luís A. Nunes Amaral, Antonio Scala, Marc Barthelemy, and H. Eugene Stanley
The article by Luís A. Nunes Amaral, Antonio Scala, Marc Barthélemy, and H. Eugene Stanley explores the statistical properties of small-world networks, which are of recent interest due to their ability to circumvent the limitations of both random networks and regular lattices in modeling complex systems. The authors identify three classes of small-world networks:
1. **Scale-free networks**: Characterized by a vertex connectivity distribution that decays as a power law.
2. **Broad-scale networks**: Characterized by a connectivity distribution with a power-law regime followed by a sharp cut-off, such as an exponential or Gaussian decay.
3. **Single-scale networks**: Characterized by a connectivity distribution with a fast-decaying tail, such as exponential or Gaussian.
The study examines various real-world networks, including technologic and economic networks (e.g., the electric-power grid of Southern California, the network of world airports), social networks (e.g., the movie-actor collaboration network, the friendship network of high school students), and biological and physical networks (e.g., the neuronal network of *C. Elegans*, the conformation space of a lattice polymer chain). The results suggest that constraints limiting the addition of new links play a crucial role in determining the nature of these networks, particularly in the emergence of scale-free and broad-scale networks. The authors also discuss the analogy between the distributions of connectivity in small-world networks and critical phenomena in statistical physics, highlighting the importance of factors like vertex aging and link costs in shaping network structures.The article by Luís A. Nunes Amaral, Antonio Scala, Marc Barthélemy, and H. Eugene Stanley explores the statistical properties of small-world networks, which are of recent interest due to their ability to circumvent the limitations of both random networks and regular lattices in modeling complex systems. The authors identify three classes of small-world networks:
1. **Scale-free networks**: Characterized by a vertex connectivity distribution that decays as a power law.
2. **Broad-scale networks**: Characterized by a connectivity distribution with a power-law regime followed by a sharp cut-off, such as an exponential or Gaussian decay.
3. **Single-scale networks**: Characterized by a connectivity distribution with a fast-decaying tail, such as exponential or Gaussian.
The study examines various real-world networks, including technologic and economic networks (e.g., the electric-power grid of Southern California, the network of world airports), social networks (e.g., the movie-actor collaboration network, the friendship network of high school students), and biological and physical networks (e.g., the neuronal network of *C. Elegans*, the conformation space of a lattice polymer chain). The results suggest that constraints limiting the addition of new links play a crucial role in determining the nature of these networks, particularly in the emergence of scale-free and broad-scale networks. The authors also discuss the analogy between the distributions of connectivity in small-world networks and critical phenomena in statistical physics, highlighting the importance of factors like vertex aging and link costs in shaping network structures.