Information Technology Reference
In-Depth Information
8.1.3.2
Cluster Linkage (CL)
The Cluster Linkage (CL) measures the overall structural change introduced by an
article
a
in terms of new connections added between clusters. Its definition assumes
a partition of the network. We introduce a function of edges œ(
c
i
,
c
j
) which is the
opposite of •
ij
used in the modularity definition. The value of œ
ij
is 1 for an edge
across distinct clusters
c
i
and
c
j
. It will be 0 for edges within a cluster. œ
ij
will allow
us to concentrate on between-cluster links and ignore within-cluster links, which is
the opposite of how the modularity metric is defined. The new metric
Linkage
is the
sum of all the weights of between-cluster links
e
ij
divided by
K
- the total number
of clusters in the network. Linking to itself is not allowed, i.e. we assume
e
ii
D
0
for all nodes. Using link weights makes the metric sensitive to links that strengthen
connections between clusters in addition to novel links that make unprecedented
connections between clusters.
It is possible to take into account the size of clusters that a link is con-
necting so that connections between larger-sized clusters become more promi-
ne
nt in the measure
ment. For example, one option is to multiple each
e
ij
by
q
si
z
e.c
i
/
si
z
e
c
j
= max .si
z
e.c
k
//. Here we define the metric without such
modifications for the sake of simplicity. Suppose
C
is a partition of G, the
Linkage
metric is defined as follows:
P
i
¤
j
ij
e
ij
K
Li nkage.G; C /
D
0; n
i
2
c
j
1; n
i
…
c
j
ij
D
The
Cluster Linkage
is defined as the difference of
Linkage
before and after new
between-clusters links added by an article
a
.
CL.a/
D
Linkage
.a/
D
Linkage
.G
baseline
˚
G
a
;C/
Linkage
.G
baseline
;C/
Linkage
(G
C
G) is always greater than or equal to
Linkage
(G). Thus, CL is
non-negative.
8.1.3.3
Centrality Divergence (C
KL
)
The Centrality Divergence metric measures the structural variation caused by an
article
a
in terms of the divergence of the distribution of betweenness centrality
C
B
(
v
i
) of nodes
v
i
in the baseline network. This definition does not involve any
partitions of the network. If
n
is the total number of nodes. The degree of structural
change
C
KL
(
G
,
a
) can be defined in terms of the K-L divergence.
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