INTRODUCTION

Social networks are the fabric of many of our interactions. Such networks include the relationships among friends and relatives with whom we share information and favors on a regular basis, and reach as far as influencing decisions by many of the world's companies regarding with whom and how they conduct their business. The many regularities in network structure across applications make a scientific study of social networks a possibility. The deep and pervasive impact that networks have on behavior makes such a study a necessity.

The science of social networks was initiated by sociologists more than a century ago, and has grown to be a central field of sociological study over the past fifty years. Over that same period, a mathematical literature on the structure of random graphs moved steadily along, with intermittent ties to the sociological literature. While economists have occasionally showed interest in networks, an explosion of studies of networks using game-theoretic modeling techniques and economic perspectives has occurred over the last decade.

A recent awakening of an interest in social networks has also occurred in the computer science and statistical physics literatures, mainly over the past five or six years. While these literatures are (slowly) becoming aware of each other, and on occasion drawing from one another, they are still largely distinct in their methods, interests, and approaches. My goal here is to provide some perspective on the research from these literatures, with a focus on the formal modeling of social networks, and to highlight some of the strengths, weaknesses, and potential synergies between the two main approaches.