Domain
complex systems, physics, network theory
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.II. THE TOPOLOGY OF REAL NETWORKS: EMPIRICAL RESULTSThe study of most complex networks has been initiated by a desire to understand various real systems, ranging from communication networks to ecological webs. Thus the databases available for study span several disciplines. In this section we review briefly those that have been studied by researchers aiming to uncover the general features of complex networks. Beyond the description of the databases, we will focus on the three robust measures of the network topology: average path length, clustering coefficient and degree distribution. Other quantities, as discussed in the following chapters, will be again tested on these databases. The properties of the investigated databases, as well as the obtained exponents are summarized inTables I and II.
This paper reviews advancements in the statistical mechanics of complex networks, emphasizing their topology and dynamics. It describes the transition from traditional random graph models to new frameworks that better capture real networks like the Internet, social networks, and cellular structures. Key findings include the identification of small-world properties, scale-free degree distributions, and the effects of network robustness against failures. The paper discusses empirical data from various systems and outlines three fundamental characteristics of complex networks: average path length, clustering coefficient, and degree distribution. It highlights existing models and analytical tools while noting the challenges of measuring and understanding the underlying organizing principles governing complex network structures and their dynamics.
This paper employs the following methods:
- Erdős-Rényi model
- Watts-Strogatz model
- Scale-free model
- Erdős-Rényi
- Watts-Strogatz
- Scale-free
The following datasets were used in this research:
- Internet
- World-Wide Web
- Movie actors
- Coauthorship network
- Biological networks
- Ecological networks
- Average path length
- Clustering coefficient
- Degree distribution
- Complex networks display small-world properties and scale-free degree distributions.
- Empirical results confirm the presence of robust organizing principles behind network topology.
- Robustness of scale-free networks varies under random failures and targeted attacks.
The authors identified the following limitations:
- The need for larger sample sizes for accurate measurement of network properties.
- The complexity of real network dynamics may not be fully captured by existing models.
- Number of GPUs: None specified
- GPU Type: None specified
complex networks
statistical mechanics
scale-free networks
small-world networks
network topology
percolation theory