# Combining with Tunable Parameters

#### Definition

It characterizes node importance according to three key factors, including node degree, the degree of node neighbors and node BC. The node importance in networks is not only related to node degree and BC, but also degree of node neighbors. Assume the importance of the node $v$ to exhibit a certain relation with "degree of neighbor nodes", "degree" and "BC of node" $v$.In this sense, $C(v)$, importance of node $v$, is defined as:

$$C(v)=\alpha d_v + \beta d_{{\lceil}_v}+\gamma B_v$$

where $\alpha$, $\beta$ and $\gamma$ are tunable parameters, and according to node role, $\alpha>\beta>\gamma$ usually. $d_v$ is the degree of node $v$ and $BC_v$ represents the betweenness number of node $v$. In mathematical formula, we use ${{\lceil}_v}$ to present the neighbor of node $v$, so $d_{{\lceil}_v}$ is defined as the total degree number of ${{\lceil}_v}$. In order to facilitate comparison between the different networks, we adopt the normalized$C_v$ By normalization, the importance of node $v$ is defined as:

$$C(v^{'})={C(v)\over {\underset{i\in N}{\sum}}C(i)}$$

where $N$ represents the scale of the network

$$C(v)=\alpha d_v + \beta d_{{\lceil}_v}+\gamma B_v$$

where $\alpha$, $\beta$ and $\gamma$ are tunable parameters, and according to node role, $\alpha>\beta>\gamma$ usually. $d_v$ is the degree of node $v$ and $BC_v$ represents the betweenness number of node $v$. In mathematical formula, we use ${{\lceil}_v}$ to present the neighbor of node $v$, so $d_{{\lceil}_v}$ is defined as the total degree number of ${{\lceil}_v}$. In order to facilitate comparison between the different networks, we adopt the normalized$C_v$ By normalization, the importance of node $v$ is defined as:

$$C(v^{'})={C(v)\over {\underset{i\in N}{\sum}}C(i)}$$

where $N$ represents the scale of the network

#### References

- Jianwei W., Lili R., Tianzhu G., 2008. A new measure of node importance in complex networks with tunable parameters. 2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008, . DOI: 10.1109/WiCom.2008.1170