Information Technology Reference
In-Depth Information
hierarchy index
of a node (see
Burt
,
2005
). The participation coefficient, like
Shannon's entropy and Burt's index, can be used to evaluate the nodes' participation
in the overall network dynamics.
In Eq. (
5.11
), we may distinguish the term involving node
v
and consider the
quantity
d
C
i
(
v
)
d
G
(
v
)
as the
representation
of node
v
within its cluster
C
i
. Similarly, we can define the
contribution
of a node
v
to its class as:
d
C
i
(
v
)
∑
u
∈
C
i
d
C
i
(
u
)
These indices have proven to be useful and complementary to Guimera's partic-
ipation coefficient and
z
-score (
Guimerà et al.
,
2005
) when analyzing community
dynamics.
5.4
Conclusion
This chapter surveyed a number of nodes and edges metrics, echoing the notions
explored in the previous chapter, and implicitly classified these metrics into a
taxonomy. Local metrics only rely on neighbor information and can usually be
computed efficiently. Distance-based metrics typically require traversing the graph
and computing all node distances. Centrality measures rely on the shortest paths
between nodes.
All of these types of metrics can help identify densely connected subgroups by
either assessing the local edge density, such as with the Jaccard index for edges
Eq. (
5.10
), evaluating the node clustering index Eq. (
5.9
), or identifying the nodes
or edges acting as bottleneck routes or points in the network. These bottleneck
elements can then be used to split the network into subgroups and capture its
community structure. The last metrics we described apply to clustered graphs and
aim to measure the degree to which a node interacts with other clusters in the
network. Examples showing how these metrics can be used to analyze networks
shall be discussed at length in the forthcoming chapters.
References
Amiel, M., Melançon, G., & Rozenblat, C. (2005). Réseaux multi-niveaux: l'exemple des échanges
aériens mondiaux de passagers.
Mappemonde
,
79
, 12 p. Retrieved July 21, 2009, from
http://
Anthonisse, J. M. (1971).
The rush in a directed graph
(Technical Rep. No. BN 9/71). Amsterdam:
Stichting Mathematisch Centrum.
Search WWH ::
Custom Search