Technological networks are physical networks that form the backbone of modern technological societies. These include the Internet, telephone networks, power grids, transportation networks, and distribution networks.
The Internet is the worldwide network of physical data connections between computers and related devices. It is a packet switched data network, meaning that messages sent over it are broken up into packets, small chunks of data, that are sent separately over the network and reassembled into a complete message again at the other end.
The format of the packets follows a standard known as the Internet Protocol (IP) and includes an IP address in each packet that specifies the packet's destination, so that it can be routed correctly across the network.
Using a packet switching model for the Internet allows computers to transmit and receive data intermittently or at varying rates without tying up capacity on the network. It also allows for a certain amount of unreliability in the network. It is not uncommon for packets to disappear on the Internet and never reach their destination, often because packets are deliberately deleted to reduce congestion in the busiest parts of the network. Only those packets of the message that are lost need be resent to complete the message. A software protocol called Transport Control Protocol (TCP), with runs on top of IP, performs the necessary error checking and retransmission automatically, without the need for intervention from computer users or other software.
The simplest network representation of the Internet is one in which the vertices of the network represents computers or other devices, and the edges represent physical connections between them, such as optical fiber lines or wireless connections. In fact, ordinary computers only occupy the periphery of the network; they are the destinations or the sources of the data flow, but they do not act as intermediate points for the flow of data between others. The internal nodes of the Internet are the routers, powerful special-purpose machines at the junctions between data lines that receive data packets and forward them toward the intended destination.
The general overall shape of the Internet is composed of three circles of vertices. The innermost circle, the core of the network, is made of high-performance routers and long-distance high-bandwidth lines. These trunk lines are the highways of the Internet, and this circle is called the backbone of the Internet. The backbone is operated by network backbone providers (NBPs). The second circle of the Internet is composed of Internet service providers (ISPs), who contract with NBPs to provide connection to the end users, the ultimate consumers of the Internet bandwidth, who form the third circle of the Internet.
The network structure of the Internet is not dictated by any central authority. In particular, one does not have to apply to any central Internet authority for permission to build a new spur on the Internet, or to make one out of service. The scheme for routing packets on the Internet is designed in such a way that if new edges or vertices are added or old ones are removed, routers will take note and adjust their routing policy appropriately.
In order to make a reliable representation of the Internet, we have to measure the Internet structure in some way. There are two primary methods for doing this: traceroute and routing tables. Traceroute is a standard tool for discovering the path taken by data packets travelling between our own computer (or any computer to which we have access) and most others on the Internet. In addition to a destination address, each packet contains a source address and a time-to-live (TTL). The TTL is a number that specifies the maximum number of steps that a packet can make to get to its destination. If the TTL of a packet reaches zero, then the packet is discarded, and a message is sent to the source computer informing that the packed was discarded and where it got to.
We can make use of this mechanism to trace the path followed by a data packed from our computer to a destination one. We repeatedly send out a packet with the destination address we are interested in and an increasing TTL (1, 2, 3, and so on). Assuming that each packet takes the same route to the destination - this may be not true if congestion happens causing the network to reroute the packet along less congested connections - then the procedure outputs a sequence of IP addresses that specifies the path from the source to the destination. The idea is to assemble a large data set of traceroute paths between many different pairs of vertices. A number of source computers, ideally well distributed over the network, is first selected. For each source, the path to a number of destination computers is computed using traceroute, obtaining a tree-like structure rooted at the source vertex. Then, a simple union of these tree-like structures gives a (not necessarily complete) snapshot of the network.
Most studies of the Internet ignore end-user computers and restrict themselves to just routers, concentrating on the inner zone of the network (backbone and ISPs). Such maps of the Internet are representations at the router level. More coarse-grained representations are created by grouping sets of IP addresses together into single vertices. These include representations at the level of subnets, domains, and autonomous systems.
A subnet is a set of IP addresses defined as follows. IP addresses consists of four numbers, each one in the range from 0 to 255, like 141.211.144.190. Addresses of the form 141.211.144.xxx form a class C subnet, addresses of the form 141.211.xxx.yyy form a class B subnet, and addresses of the form 141.xxx.yyy.zzz form a class A subnet. Since all the addresses in a class C subnet are usually allocated to the same organization, a reasonable way of coarse-graining Internet network data is to group vertices into class C subsets and place an edge between two subnets if any router in one has a connection to any router in the other. A domain is a group of computers and routers under the control of a single organization and identified by a domain name like uniud.it. Finally, an autonomous system is similar to a domain: it is a collection of computers and routers, usually under single administrative control, within which data routing is handled independently of the wider Internet, hence the name autonomous system.
Coarse-graining at the autonomous system level is not done with data derived from traceroute sampling but with data based on routing tables. Internet routers maintain routing tables that allow them to decide in which direction incoming packets should be sent to best reach their destination. They consist of lists of complete paths from the router in question to destinations on the Internet. In theory routers need store only the first step of the path; in practice they save the entire path to the destination for efficient calculation of routes. In fact, routing tables in routers are represented at the level of autonomous systems. This is sufficient since data passing within the autonomous system is handled autonomously by the system, while data passing among autonomous systems is handled at the Internet-wide level using Border Gateway Protocol (BGP). In order to get a reasonable snapshot of the Internet, a set of router tables is collected, each containing a large number of paths starting from a single autonomous system containing the source router. The union of these router tables gives a not necessarily complete snapshot of the Internet at the autonomous system level. As with traceroute, it is important that the source routers are well scattered over the network to avoid duplication of paths and of work.
The telephone network is made of landlines and wireless links that transmit telephone calls. It is important to realize that even calls made on wireless phones are still primarily carried over the traditional landline telephone network. The signal from a wireless phone makes the first step of its journey wirelessly to a nearby transmission tower, but from there it travels over ordinary phone lines.
By contrast with the Internet, the traditional telephone network is not packed switched. Instead, the telephone network is circuit switched, which means that the telephone company has a number of lines or circuits available to carry telephone calls and it assigns then to individual callers. In the earliest days of the telephone systems the lines actually were individual wires, one for each call the company could carry. Later, phone companies have employed techniques for multiplexing phone signals, that is, sending many calls down the same wire simultaneously. The exception is the last mile of connection to the individual subscriber, which usually carries one phone call at a time.
The telephone network has a three-tiered design. Individual telephone subscribers are connected over local lines to local telephone exchanges, which are connected over shared trunk lines to long-distance offices. Long-distance offices are then connected among themselves by further trunk lines. This structure is, in many ways, rather similar to that of the Internet. Local phone calls can be handled by the local exchange alone and do not need to make use of any trunk line.
Today most of the telephone network is no longer circuit switched. Instead, it is a digital packet switched network like the Internet, with voice calls digitized, broken into packets, and transmitted over telephone or optical fiber links. Only the last mile of lines is still carried on an old-fashioned dedicated circuit, and even the situation on the last mile is changing with the advent of Internet phone services (voice on IP), which send voice calls over the Internet rather than over dedicated telephone lines. Hence the Internet and the telephone network are not disjoint networks, and it may not be long before the telephone and the Internet networks merge into a single network.
A power grid, in this context, is the network of high-voltage transmission lines that provide long-distance transport of electric power within and between countries. Low-voltage local power delivery lines are normally excluded. The vertices of a power grid correspond to generating stations and switching substations, and the edges correspond to the high-voltage lines.
Failures on power grids may have cascading effects: the failure of one node may recursively provoke the failure of connected nodes. This behaviour can give rise to surprising results such as the observed power-law distribution in the sizes of power outages.
Transportation networks include airline routes and road and rail networks. Distribution networks include oil and gas pipelines, water and sewerage lines, and routes used by the post office and package delivery companies.
One class of distribution networks that has been relatively well studied is river networks, where the edges are rivers or streams and the vertices are their intersections. Of particular note is the fact that river networks, to an excellent approximation, take the form of trees. That is, they contain no loops, so water at any point of the network drains off via a single path. Similar in some respects to river networks are networks of blood vessels in animals and their equivalent in plants.