<s>
In	O
network	O
science	O
,	O
reciprocity	B-Protocol
is	O
a	O
measure	O
of	O
the	O
likelihood	O
of	O
vertices	O
in	O
a	O
directed	O
network	O
to	O
be	O
mutually	O
linked	O
.	O
</s>
<s>
Like	O
the	O
clustering	O
coefficient	O
,	O
scale-free	O
degree	O
distribution	O
,	O
or	O
community	O
structure	O
,	O
reciprocity	B-Protocol
is	O
a	O
quantitative	O
measure	O
used	O
to	O
study	O
complex	O
networks	O
.	O
</s>
<s>
Second	O
,	O
when	O
analyzing	O
directed	O
networks	O
,	O
people	O
often	O
treat	O
them	O
as	O
undirected	O
ones	O
for	O
simplicity	O
;	O
therefore	O
,	O
the	O
information	O
obtained	O
from	O
reciprocity	B-Protocol
studies	O
helps	O
to	O
estimate	O
the	O
error	O
introduced	O
when	O
a	O
directed	O
network	O
is	O
treated	O
as	O
undirected	O
(	O
for	O
example	O
,	O
when	O
measuring	O
the	O
clustering	O
coefficient	O
)	O
.	O
</s>
<s>
Finally	O
,	O
detecting	O
nontrivial	O
patterns	O
of	O
reciprocity	B-Protocol
can	O
reveal	O
possible	O
mechanisms	O
and	O
organizing	O
principles	O
that	O
shape	O
the	O
observed	O
network	O
's	O
topology	O
.	O
</s>
<s>
However	O
,	O
this	O
definition	O
of	O
reciprocity	B-Protocol
has	O
some	O
defects	O
.	O
</s>
<s>
It	O
cannot	O
tell	O
the	O
relative	O
difference	O
of	O
reciprocity	B-Protocol
compared	O
with	O
purely	O
random	O
network	O
with	O
the	O
same	O
number	O
of	O
vertices	O
and	O
edges	O
.	O
</s>
<s>
The	O
useful	O
information	O
from	O
reciprocity	B-Protocol
is	O
not	O
the	O
value	O
itself	O
,	O
but	O
whether	O
mutual	O
links	O
occur	O
more	O
or	O
less	O
often	O
than	O
expected	O
by	O
chance	O
.	O
</s>
<s>
In	O
order	O
to	O
overcome	O
the	O
defects	O
of	O
the	O
above	O
definition	O
,	O
Garlaschelli	O
and	O
Loffredo	O
defined	O
reciprocity	B-Protocol
as	O
the	O
correlation	O
coefficient	O
between	O
the	O
entries	O
of	O
the	O
adjacency	O
matrix	O
of	O
a	O
directed	O
graph	O
(	O
if	O
a	O
link	O
from	O
i	O
to	O
j	O
is	O
there	O
,	O
and	O
if	O
not	O
)	O
:	O
</s>
<s>
The	O
new	O
definition	O
of	O
reciprocity	B-Protocol
gives	O
an	O
absolute	O
quantity	O
which	O
directly	O
allows	O
one	O
to	O
distinguish	O
between	O
reciprocal	O
(	O
)	O
and	O
antireciprocal	O
(	O
)	O
networks	O
,	O
with	O
mutual	O
links	O
occurring	O
more	O
and	O
less	O
often	O
than	O
random	O
respectively	O
.	O
</s>
