Jellyfish, and other
Interesting creatures
Of the Internet
Scott Kirkpatrick, Hebrew University
with
Avishalom Shalit, Sorin Solomon,
Shai Carmi, Shlomo Havlin,
Eran Shir, and Yuval Shavitt
TAU seminar, 6 November, 2005
Copyright, Pixar, Inc. 2003
DIMES – Internet topology map
•
Previous efforts to measure the Internet have used:
– One machine + Traceroute to many destinations
– Many* machines, specially deployed to traceroute to many destinations
• * Many <= 50 because of management headaches
• Sites restricted to academic or gov’t labs, on network backbone
• General perception was that Law of Diminishing Returns has set in
•
http://www.netdimes.org seems to have made a breakthrough
– Don’t manage machines, offer a very lightweight, limited purpose client, and
collect its measurements centrally
• 100 – 1000 clients via word-of-mouth (Sep04 to April05)
• 1000 – 5000 clients achieved via press, slashdot, still in the geek community
– (May05 -- ?)
• 5000 – 50000 clients in the general public by offering services in return
– Somewhere in the 5000-10000 client range, we have the network monitoring
itself, and the possibility that it can also manage itself in real time.
AS map for July 2005
BGP
• 20585 nodes
• 45720 edges
• <k> = 4.44
DIMES
• 14332 nodes
• 60134 edges
• <k> = 8.39
33,862 edges
+
11,858 edges
81,672 edges
<k> > 7.80
24,182 in both maps
35,952 new edges
Exploring the DIMES AS-graph
•
•
We consider the Internet at the level of its autonomous systems (ASes)
Previous studies have used degree as indicator to decompose networks
– In particular, the Faloutsos’ “jellyfish model”
• Identify core of network as maximal clique (not a robust criterion)
• Shells around network labeled by hop count from core (a small world)
• Find that sites with few links often connect to those with high degree
•
•
We consider longer-range connectivity, using k-pruning.
K-core, K-shell, and K-crusts result
– K-shell is “derivative” of K-core, K-crust is union of K-shells
– Near power-law structure of a new “inflow” region is observed
– K-shells are not connected, but K-crusts have a giant cluster
•
For Erdos-Renyi graphs, K-core is w.h.p. K-connected. For scale free?
•
Result – focus attention on the capabilities of the inflow region, in support of
P2P, chat, local traffic.
Next steps – reachability is much harder than percolation.
•
How does original degree map into k-shell?
AS K-shell decomposition
IP K-shell decomposition
K-shell decomposition
K-crusts show percolation threshold
 These are the hanging
tentacles of our (Red Sea)
Jellyfish
Largest cluster in each shell
Data from 01.04.2005
Distribution of flows in the nucleus
Now offering: monthly public stats
K-shell for network visualization
Using LaNet-Vi
http://xavier.informatics.indiana.edu/lanet-vi
Michalis Faloutsos’ Jellyfish
Shells
3
2
1
Core
• Highly connected nodes
form the core
• Each Shell: adjacent nodes
of previous shell, except 1degree nodes
• Importance decreases as
we move away from core
• 1-degree nodes hanging
• The denser the 1-degree
node population the longer
the stem
Meduza )‫ (מדוזה‬model
In January, the inner core was at K = 30, but this picture
persists to the present day, when core is >40. The precise
definition of the tendrils: those sites isolated from the
largest cluster in all the crusts – they connect only to the core.
Links per site of k-shells
to k-core (above) and to k-crust (below)
Where do the links go in Medusa?
Early shells (1-10) link to intermediate shells as well as to the core.
Average distance between sites in a crust
Percolation “attacks”
Random scale-free graphs produce the
same structure
• Seen in both Barabasi-style and Molloy-Reed models of scale
free networks
Next steps
• New data permits reexamining the clustering behavior
– Much data not seen in previous BGP-based studies
– This is the major deviation from simple random models
– Analyze as a function of k-shell, instead of simply degree
• Reachability is not percolation, but can be evaluated
– Decision to transmit a message depends on sender and
destination, not simply on the existence of a link
– Cost of evaluating uphill-downhill reachability is comparable to
shortest path
Preliminary reachability data (std data set)
Now add sideways steps at top of path
Now restrict to the 20-crust
Sideways step less effective inside crust