“topology of the Internet” or “Internet graph” have entered the mainstream science literature, even though
they are essentially meaningless without precisely-stated definitions. For one, “Internet topology” could
refer to the connectivity structures encountered in any of layers in the protocol stack, or at various levels
of aggregation. Common examples are
1. Router-level (layer 3):
An often sought topology is the router level. Somewhat ambiguously, this
may also be called the network level, or IP level, but “network” is a heavily overloaded term here,
and the IP level can also be ambiguous. For instance, IP level could refer to the way IP addresses
are connected, that is it could refer to the interfaces of one router as separate nodes [19], but that is
rarely what is useful for network operations or research. We could also add at layer 3, in addition to
interface-level topology described above, the subnet-level topology [19,67,81,148,149], describing
the interconnectivity of logical subnets (often described by an IP-level prefix), but here we focus on
the more commonly considered router level.
The router-level graph shows a range of interesting implementation details of a network. This type
of information is critical for network management applications, as much of Internet management
rests at the IP layer, and it is of great importance for network adversaries. For instance, developing
tools to measure network traffic requires an understanding of the router-layer topology, in order to
match traffic to links. Similarly traffic engineering, and reliability analyses are carried out at this
level. One complication of this layer is that we sometimes wish to obtain the topology extending
out to end-hosts, which are not technically routers, but we shall include these in our definition of
router-layer topology, unless otherwise specified.
2. Switch-level (layer 2):
A single IP layer logical link may hide several layer-2 devices (hubs and
switches). The increasing prevalence of Ethernet, and the ability to provide redundancy at rea-
sonable cost, has led to a proliferation of such devices, and most Local Area Networks (LANs) are
based around such. Hence, very many networks which have trivial, or simple IP layer topologies
have complex and interesting layer-2 topologies. Multi-Protocol Label Switching (MPLS) further
complicates the situation by creating logical layer-2 networks without physical devices, often in the
form of cliques. Measurements often see only one layer, creating misunderstandings of a network’s
true resilience and more general graph properties. For instance, layer-2 devices can connect large
numbers of routers, making them appear to have higher degree at layer-3 [104] (for more detailed
discussion see §3.2.3).
3. Physical-level (layer 1):
Below the link layer (layer 2), lies the physical layer. Again, many physical
devices may underly a single logical link. Discovery of this layer is of critical importance in network
management tasks associated with reliability. In particular, the concept of Shared Risk Link Groups
(SRLG) requires knowledge of which links are carried on which fibers (using Wavelength Division
Multiplexing), in which conduits. If a backhoe digs up a single conduit, it will cause a bundle of
fibers to fail, and so connections that are in the same SRLG will all fail simultaneously. Clearly
redundant links need to be in different SRLG, and discovery of the physical topology is important to
ensure that this is the case.
4. PoP-level:
A Point-of-Presence (PoP) is a loosely defined grouping of devices, often defined by a
metropolitan area. PoP level topologies are quite useful, essentially because these graphs describe
the logical structure of the network as the designer intended, rather than its particular implementa-
tion in terms of individual routers. Such topologies are ideal for understanding tradeoffs between
connectivity and redundancy, and also provide the most essential information to competitors or
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