2002/04/30 by Vito Latora, Massimo Marchiori · 780 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Artificial intelligence #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Complex network #Complex system #Computer science #Data science #Economics #Geography #Management science #Mathematics #Network science #Operations research #Realm #Scale (ratio) #Small-world network #Variety (cybernetics) #World Wide Web #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2003-00095-5
published in The European Physical Journal B 32(2), 249-263 (Springer Science+Business Media) · 17 pages, 10 figures, 4 tables
arxiv created 2002/11/12 · openalex publication_date 2003/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation suffers from a variety of limitations, that make it unsuitable to provide a general tool of analysis for real networks, and not just for mathematical (topological) abstractions. In this paper we show where the major problems arise, and how there is therefore the need for a new reformulation of the small-world concept. Together with an analysis of the variables involved, we then propose a new theory of small-world networks based on two leading concepts: efficiency and cost. Efficiency measures how well information propagates over the network, and cost measures how expensive it is to build a network. The combination of these factors leads us to introduce the concept of \em economic small worlds, that formalizes the idea of networks that are "cheap" to build, and nevertheless efficient in propagating information, both at global and local scale. This new concept is shown to overcome all the limitations proper of the so-far commonly adopted formulation, and to provide an adequate tool to quantitatively analyze the behaviour of complex networks in the real world. Various complex systems are analyzed, ranging from the realm of neural networks, to social sciences, to communication and transportation networks. In each case, economic small worlds are found. Moreover, using the economic small-world framework, the construction principles of these networks can be quantitatively analyzed and compared, giving good insights on how efficiency and economy principles combine up to shape all these systems.