When crickets chirp, they tend to synchronize, such that their oscillating cycles phase together and evolve into shared patterns. The resulting sound can easily be heard and verified, but tracing the effect back to its cause is a murky process, since no single cricket can be identified as the decisive pacesetter. Instead, groups of similarly timed chirps from different crickets link up coincidentally, and when the conjoined noises accumulate enough volume, others begin following the swelling pattern. Figuring out the math behind such a random group process is the business of network theory, a nascent science that gets a laudable overview in Duncan J. Watts' *Six Degrees*. Falling in place behind Malcolm Gladwell's *The Tipping Point *and Steven Johnson's *Emergence*, the book shows math and science staring down complex phenomena that fit, however stubbornly, into network structures. From airline schedules to power-grid blueprints to the personal ties comprising the so-called "six degrees of separation," network models help govern the current worldview of numerous disciplines, from biology and physics to economics and sociology. Telling a story "about science in the making," Watts traces how disparate fields helped shape network theory into its increasingly defined mold, which stretches to relate how network structures influence their components, and vice-versa. Crucial to the study is the notion of the "critical level" or "phase transition," the point when random occurrences careen toward something shared and communal. Critical levels show up in pure mathematical graphs much the same as they do in representations of stock-market growth and disease epidemics; random data of any kind has a way of congealing into shared patterns when viewed from the right vantage point. Interpreting those patterns with any precision is still a long way from network theory's grasp, but *Six Degrees* makes the process into a colorful game, when it's not grinding through mathematical processes. As a discipline that takes nothing and everything at face value, network theory has a lot to account for, so many of its "eureka!" moments merely confirm intuitive ideas. But while some of *Six Degrees*' assertions prove elementary when the impressive math fades, others give hard-science grounding to ideas that otherwise defy logic. Some network models seem screamingly reductive when applied to fields like sociology, but, as Watts writes, "While groups can be categorized easily, individuals cannot." Network theory is structuralist by design, but it also willfully joins groups and individuals in their Heisenbergian dance of uncertainty. Parts of *Six Degrees* read like a how-to manual for steps that suffer under scrutiny, but Watts' inviting approach shapes its ordered moves into a package more dashing than dry.