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two variables given the rest of the variables in blocks k and l. If the conditional asso-
ciation between variables i and j in blocks k and l is significant, an arrow pointing
from k (blocks with lower index) to l (blocks with higher indices) is plotted. Like-
wise, the fitting continues until all significant direct associations between variables
within each block and between any two blocks are determined. Figure
.
, which is
reproduced from Fig.
.
of Aburatani et al. (
), depicts the interactions of pseu-
dogeneswithinandbetween phases.hecausal relationship betweenvariables inone
phase to those in a latter phase is illustrated more clearly by a chain graph, for exam-
ple Fig.
.
c,than by formula and tables. Moreover, a graph also clearly demonstrates
whichgeneisthehighlyconnected“hubgene,"forexample C
,
in G
among the four
pseudo-genes.Hubgenesarelikelytobeimportant becauserandommutations inor-
ganisms lacking thesegenes wouldlikely leadtofitness defects.Bycomparing graphs
of genetic networks among different species, one mayinfer whichhub genes arecon-
served; this maylead toimportant applications tocomplex diseases inhumans. Tong
et al. (
) observed that synthetic genetic interactions have the property that the
connectivity of genes follows a powerlawdistribution. Namely,many genes have few
interactions and a few genes have many interactions. Networks of the World Wide
Web (WWW) and protein-protein interactions also share this power law property.
Figure
.
c also shows that graphs can help to identify networks whose connectiv-
ity distributions follow the powerlaw. Further, graphical similarity may indicate that
analytic methods applied in the area of the WWW can also be applied to the areas of
genetic and protein-protein interactions.
Figure
.
.
Chain graphs used to depict genetic interactions within and across phases
