Inferring network properties from topological and spectral analysis

Self-organized complex systems can be analyzed in terms of their topological structure. This can unveil relevant properties related to robustness and efficiency. We show how a suitable combination of topological and spectral analysis may improve the understanding of the mechanisms and the driving force which lead to the spontaneous formation of the internet network at the Autonomous System level. Introduction In the last 20 years, communication and information technology have undergone an impressive speed-up which has driven to a communication-biased form of social progress. Computers, telephones, televisions, domestic appliances and cars contain a number of electronic devices for the exchange of information and data, enabling “intelligent” services designed for a maximum efficiency and user comfort. World is extremely interconnected; however, more than ever, interconnection relies on the integrity of complex networks, including the Internet, telecommunications, electric power systems, oil and gas networks, rail and road networks, etc. All these complex networks have some common properties and are being investigated by different scientific communities. Complex systems are functional structures sharing the property of being self-generated (i.e. grown under any external supervision) under the action of some "functional" driving force. Although related to a variety of domains (biology, sociology, telecommunications, ethology etc.), they appear to share a number of properties (common topology, common functional assets, robustness, self-healing etc.) whose nature and "necessity" are key points it is worth investigating with the aim of: (a) understanding the nature of the generating driving forces and the details of the growth mechanisms; (b) control, duplicate and/or transpose into different domains, under the form of technological objects, naturally-occurring structures and functions aimed at producing and controlling "complex" man-made systems. Results and advancements in fundamental and technological areas are seldom cross-fertilizing each other. Lack of common languages, decades of incommunicability and attention to different properties and functions of systems, have inhibited the flow of methods and results from one field to the others. It is now time to export the most recent acquisitions (methods, tools, paradigms), which have lead to a dramatic improvement of the knowledge in some domains of basic science (physics, biology) into technological domains where they might have an high functional impact. The field of analysis and protection of "Large Complex Critical Infrastructures" (LCCI), such as an electric grid, a telecommunication network, a railway/air/road transportation network, an information network, a social network, etc. might highly benefit from recent theoretical advancements [1,2]. These are "complex systems"; as such, they might be thought, after all, as made up by the superposition of interacting sub-units whose internal complexity is intrinsically similar to that of the whole. If, on one side, the theory of system control has developed its own strategies and methods, on the other side new ideas and "solutions" are emerging in the area of statistical mechanics [1,2]; these ideas have been promptly applied to several other domains, such as Cell Biology, Sociology etc. [3-5]. In Cell Biology, for instance, cells are seen as multi-functional systems capable of producing different response to a practically infinite variety of inputs [3,4]. They have been analyzed in general terms and many interesting unveiled properties have been discovered [3]. Problems are thus reconducted to a unifying theoretical frame and analyzed therein with same methods and tools. We have attempted to analyze, under this unifying perspective [2] and following an extensive seminal paper on the argument [6], data of the topological structure of the internet in US, at the Autonomous System (AS) level. The analyzed data are snapshots of that network, resulting from a daily collection of BGP (Border Gateway Protocol) routing tables coming from a route server with BGP connections to multiple geographically distributed target operational routers [7]. This system represents an example of a complex infra -structure undergone a sizeable growth in the last few years, thus allowing the study of its growth process.