# Epidemic Centrality

#### Definition

The principal hypothesis is that the node which is highly ranked as a “superspreader” for some disease spreading parameters (i.e. in some disease spreading regime) may not be highly ranked for some other epidemic parameters (i.e. in some other epidemic regime).

$$Z^i=\int_0^1 dp \int_0^1 dp w(p,q)X_{p,q}^i$$

were $Z^i$ is epidemic centrality, the quantity of $X_{p,q}^i$ is the average numbers of infected nodes normalized to the total number of nodes in the network for parameters $pq$, $p q$ are parameters of the disease spreading model (properties of the disease in the SIR epidemic model). $w(p,q)$ is nonuniform weight function. All available additional information on the epidemic risks posing a threat should be incorporated into that function

$$Z^i=\int_0^1 dp \int_0^1 dp w(p,q)X_{p,q}^i$$

were $Z^i$ is epidemic centrality, the quantity of $X_{p,q}^i$ is the average numbers of infected nodes normalized to the total number of nodes in the network for parameters $pq$, $p q$ are parameters of the disease spreading model (properties of the disease in the SIR epidemic model). $w(p,q)$ is nonuniform weight function. All available additional information on the epidemic risks posing a threat should be incorporated into that function