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A complex network is a graph model of an interacting system whose connectivity has nontrivial structure relevant to its behavior. The phrase does not specify one mathematical graph class: degree heterogeneity, clustered neighborhoods, community organization or changing connectivity may be important depending on the application.

For example, two graphs can have the same numbers of vertices and edges but very different shortest-path graph distances. A six-cycle has average degree two and diameter three; two disjoint triangles also have average degree two but lack paths between the two components. Their equal mean degree conceals a decisive connectivity difference.

Network science therefore uses several measurements and compares them with explicit random graph models. Labels such as small-world network or scale-free network express additional quantitative hypotheses; they should be tested rather than inferred merely because a diagram looks complicated.

Réka Albert is a physicist whose work connects network science with biological networks. With Albert-László Barabási, she coauthored the 1999 paper introducing a growing preferential attachment model for the emergence of broad degree distributions, now called the Barabási-Albert model.^[ref]

Her biological work uses logical models to connect the structure of a regulatory graph with its possible dynamical states. Such models represent interactions without requiring a measured kinetic constant for every reaction. Her institutional profile describes research on mechanisms controlling complex-network dynamics and on predictive modeling of biological systems.^[ref]

Homepage: www.ralbert.me/