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A random network model which allows for tunable, quite general forms ofclustering, degree correlation and degree distribution is defined. The model isan extension of the configuration model, in which stubs (half-edges) are pairedto form a network. Clustering is obtained by forming small completely connectedsubgroups, and positive (negative) degree correlation is obtained by connectinga fraction of the stubs with stubs of similar (dissimilar) degree. An SIR(Susceptible -> Infective -> Recovered) epidemic model is defined on thisnetwork. Asymptotic properties of both the network and the epidemic, as thepopulation size tends to infinity, are derived: the degree distribution, degreecorrelation and clustering coefficient, as well as a reproduction number $R_*$,the probability of a major outbreak and the relative size of such an outbreak.The theory is illustrated by Monte Carlo simulations and numerical examples.The main findings are that clustering tends to decrease the spread of disease,the effect of degree correlation is appreciably greater when the disease isclose to threshold than when it is well above threshold and disease spreadbroadly increases with degree correlation $\rho$ when $R_*$ is just above itsthreshold value of one and decreases with $\rho$ when $R_*$ is well above one.

A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon