Recently, complex networks have drawn increasing interests. It is often convenient to regard this research area to be composed of studies of network structure and network functions. Studies of network structure are concerned about topological characteristics of complex networks such as the small-world and scale-free properties. Studies of network functions deal with processes and phenomena on complex networks such as virus propagation. This article is a minireview of complex networks from these dual viewpoints.

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It is well known that the Hamiltonian formalism plays a central role in classical mechanics. In this article, we introduce the notion of gradient/skew-gradient structure which enables us to apply the Hamiltonian formalism for studying pattern formation problems in dissipative systems. We explain usefulness of the gradient/skew-gradient structure through the linear stability analysis of standing pulse solutions and spatially periodic stationary patterns in reaction-diffusion equations, which are typical subjects of pattern formation theory in disspative systems.

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