1. Royi Itzhack

2.  Large number of
“interactomes” are currently
accumulated.
 These interaction networks
combine measurements from
a large number of sources to
produce a network of
interactions.
 We here assume that the
network is only characterized
by the graph of interactions
and nothing is known about
the content of the nodes.

3.  Interactomes occur in
biology:
• protein networks.
• genetic networks. neural
networks.
 in social sciences
• Social networks
 In information
• Wikipediae
• Content networks
 Most such networks are
not validated and contain a
large amount of
superfluous data.

4.  We are looking for important features in
the networks.
 These features can be:
1. Important nodes.
2. Information flow.
 We propose algorithms to extract those
from the network topology and methods
to validate the results.

6.  We compared the ratio of scores of two
neighboring nodes, and define that a node is
higher in hierarchy than its neighbor and if its
score is higher and the score ratio is between the
lower and upper thresholds.
 For many neighboring nodes there is no
hierarchical relation. Their score ratio can be too
close to one and thus above the upper threshold
(e.g. cheese and meat).
 Their ratio could also be too far from one and
thus below the lower threshold (e.g. Obama and
myself)

7. • The Hierarchy score is the centrality normalized to the
indegree and the outdegree.
• We checked whether the nodes participation in
information flow on the network (betweenness) is higher
or lower than what is expected merely from its
connectivity.
CB (i)
H (i)
(kin (i) 1)(kout (i) 1)

8. •The score is proportional only to the local neighberhood
•Very fast – low CPU and memory cost
•Average 82%
kin kout
H (i) kin kout
(kin kout ) (kin kout )
Problem : the algorithm is not sensitive to the network structure
for example: for binary tree the algorithm is inefficient

9. Nin (m) m N out (m) m
H (i) /
m Nin (m) m N out (m)
Nin (i) number of incoming neighbours of level m
Nin (i) average number of neighbours of level m
weighted base

11.  As we decrease the upper
threshold, we reduce the
fraction of node couples for
which a hierarchical position
can be obtained
 On the other hand, we
increase the success rate for
the remaining node couples.
 Low upper cutoff leads to a
tight definition of the
hierarchy, with practically all
edges in the proper
direction, but with a low
number of categorized edges,
 High upper cutoff leads to a
hierarchy, which is often
unnatural.

13.  Microsoft Windows XP Pro operating system.
 Links are directional and that the obtained network is
practically acyclic,
 Using the attraction basin hierarchy 6869 links out of
6899 (99.57%) were marked in the proper direction.
 local hierarchy producing 98.57% of properly
computed links,
 PageRank with 96.13%.
 HITS 90%
 The centrality-based hierarchy 63%

16.  Isthere a
meaningful
information flow
between nodes in
networks?
 Specifically, can we
extract from the
network the
meaningful paths of
information?

18.  Ifinformation flows, it should be sensitive
to the precise direction of each edge.
 We thus checked what happens when the
direction of edges is flipped.
 Strangely nothing changes in the network
except for two things:
 The distance distribution gets slightly
shorter.
 The circle distribution length gets
drastically shorter.

21.  The long circles include a well defined
limited number of essential genes/neurons.
 In the neural network these neurons map
to the main trajectories from the sensor to
the interneuron circles to the motor
neurons.
 In genetic network these trajectories relate
the most essential genes (genes that their
deletion leads to organism death).

22. A simple toy network explains the
observed results.

23.  The spaghetti ball of networks can be
replaced by clear hierarchies or organized
information pathways.
 The vast majority of edges can be removed
while maintaining the important information
flow.