network. The incoming degree gives the number of links pointed to
the target node. The outgoing degree presents the number of
connections from the target node to others. The degree distribu-
tion (p(n)) gives probability of a node having n links. For many
gene regulatory networks, they have modular structure, and genes
of these networks take effect in a cluster manner [16, 29]. For these
networks, they are regarded as scale-free networks in mathematics,
and their degree distributions are in accordance with a power-law
distribution,p(n)~nγ, whereγthe is the degree exponent. The
smaller the value ofγ, the higher probability of modular structure
the network has. Another elementary concept of nodes in network
is path length, which gives the number of links needed to pass
through for traveling between two nodes. The shortest path length
(l) presents the minimum value of all possible paths between two
nodes. The value of shortest path length from node A to B is
equivalent to that of B to A in an undirected network. However,
the value of shortest path length from node A to B may be different
to that of B to A in a directed network. In general, the clustering
coefficient is adopted to characterize the tendency of nodes in
network to form clusters and modules [16]. For an undirected
network, assuming a node A has n links to other nodes, then its
clustering coefficient is defined asca¼ 2 ma/n(n1), wheremais
the number of links connectingnneighbors of node A to each
other. The mean value of clustering coefficient for nodes with n
links, termed asc(n), depicts clustering property of the network.3.1 Identification
of Hub Genes
in Networks
In many GRNs, they present scale-free characteristics, and most
links are connected to a few nodes, which determine structure
property of the network in a certain degree [30]. These genes are
regarded as central nodes or hubs. It is imperative to identify hub
genes in GRNs since these genes play important roles in regulatory
patterns of networks. In practice, centrality of a node is defined by
the betweenness measure, which gives the number of shortest paths
passing through the node. The higher the value of betweenness, the
more important the node is. As term of GRNs, the hub genes
encode essential regulators, like transcription factors, which regu-
late expression level of many downstream target genes.3.2 Identification
of Gene Modules
and Motifs
in Networks
In most GRNs, genes work together in a modular manner to
achieve a distinct function for internal and external stimuli. In a
module or cluster, there are high connections between nodes and
can be reduced to many triangle sets [16, 31, 32]. A high triangle
density can be expressed by a big value of clustering coefficient.
Therefore, biologist can estimate modular level of a network
through calculating the mean value of clustering coefficient. After
identifying hub genes in GRNs, the functional partners of these
genes can be revealed through module analysis since they work
together with hubs. In the past 20 years, some module mining144 Guangyong Zheng and Tao Huang