Information Technology Reference
In-Depth Information
residential block as dormitory, one could first calculate the fraction of edges having
the same residence location. It is calculated as follows:
,
.
.
||
where,
represents the value
a
for a node
i.
In other words, we are identifying the
total number of matched nodes with the same attribute values for an attribute
a. E
represents the total number of edges. Next, we calculate
E
A
which represents the
expected value when attributes are randomly assigned.
1
||||1
∑
where,
T
represents the number of nodes with each of the possible
k
attribute values
and U is the sum of all
T
nodes, i.e.,
U
∑
T
. The ratio of the two is known as
affinity
:
/
. This measure is then used to discover “attribute level communi-
ties”, that is, subgraphs with high affinity. Either the affinity of a whole network
could be compared with another, or this can be used to identify communities in
simulated and observed networks.
Silo Index.
This index identifies the proportion of edges between nodes with the same
attribute value in a network. If all the nodes that have a value
Y
for an attribute only
have links to other such nodes, and not to nodes with any other values for that
attribute, it implies that a strong community exists, which is disconnected from the
rest. Such a set would have a maximum value of this index. In short, this index helps
us identify how cohesive inter-attribute edges are. It ranges from -1 to 1, for the ex-
treme cases (no in-group edges to only in-group edges respectively) and can be writ-
ten as
/
, where
I
is the number of internal edges and
E
the number of
external edges. It is quite similar to the E-I index [23] but with an opposite sign.
5
Dynamic Networks
Most, if not all, agent-based models of social networks assume a fixed-sized popula-
tion of agents, which makes it easier to compare networks across time as only the ties
change during the simulation, i.e., the '
n
' denoting the size of nodes in the networks
remains fixed. The analysis and validation of networks becomes more difficult when
the underlying network changes with respect to the individuals, which, in addition to
the dynamics of interactions, affects the edge set. Depending upon the phenomenon
being simulated agents may leave or join the networks over a course of a simulation.
Consequently, it is possible that the shape and size of the network at any time
t
i
could
be radically different from that at any later time
t
j
, (
i< j
). This is also almost inevitable
for many real social networks that are observed at different times.
Techniques such as Quadratic Assignment Procedure (QAP) have been used in
comparing longitudinal networks. QAP is nonparametric and thus unlike the
t
-test,
requires no
a priori
assumption about the distribution of the observed data [22].
