By deJardins, Marie; Gaston, Matthew E.; Radev, Dragomir
AI Magazine , Vol. 29, No. 3
Most people ... would agree that a fundamental property of complex systems is that they are composed of a large number of components or "agents," interacting in some way such that their collective behavior is not a simple combination of their individual behaviors.
The importance of networks permeates the world today. From biology to social systems, from the brain to the Internet, networks play an important and central role in the way the world works. In the last 10 years, due in part to large increases in computational power, large-scale, real-world networks have received much attention from a variety of fields of study.
Within the artificial intelligence community, networks appear in some form in nearly every subdiscipline: knowledge representation, inference, learning, natural language processing, multiagent systems, analogical reasoning, and many others. The goals of this special issue are to provide a sampling of research efforts focused on how networks can be used in AI systems and to facilitate cross-communication among subdisciplines that are studying networks from different perspectives.
The seven papers we include here cover a broad range of network-inspired AI research--in natural language processing, data mining, the semantic web, peer-to-peer networks, multiagent systems, analog networks, and the modern social network of the "blogosphere." Each article represents a snapshot of the area it describes; for example, the collective classification problem surveyed by Prithviraj Sen, Galileo Namata, Mustafa Bilgic, Lise Getoor, Brian Gallagher, and Tina Eliassi-Rad is just one of many problems within the emerging research area of link mining. Moreover, networks are influential in many other areas of AI that are not represented here, including Bayesian networks and graphical models, sensor networks, swarm systems and cellular automata, graphical games, trust and reputation systems, and computational organizational design.
Table 1 summarizes the articles in this collection by characterizing the nature of the networks that are the focus of each of the seven papers.
Basic Graph Theory
In reading the articles presented here, some basics of graph and network theory may be useful for the reader who is not familiar with these terms. We start with some basic terminology.
A graph G is defined to be a pair (V, E), where V is a vertex set and E is an edge set (see following). The terms graph and network are often used interchangeably.
The finite vertex set V is a set of descriptors for the vertices in the graph. Each vertex may just have an identifier, or it may have an arbitrarily complex set of attributes. The terms vertex and node are often used interchangeably. Depending on the application, nodes may also be referred to as agents or entities.
The finite edge set E specifies the relationships between the vertices in the graph. Each edge e c E is a pair of vertices, which are called the endpoints of the edge. Edges may be ordered or unordered and also weighted or unweighted. A hyperedge may connect more than two vertices. Edges are often used to represent relations.
The degree of a node, [k.sub.i], is the number of edges that are connected to node i. In directed graphs, degree can be broken down into "in-degree" (number of edges coming into the node) and "out-degree" (number of edges pointing out of the node).
A number of properties prove to be useful in graph theory and social network theory for analyzing and understanding the behavior of graph structures.
The path length between two nodes is the minimum number of edges that must be traversed to move from one node to the other in the graph. The average path length is an average across all pairs of nodes in the graph.
Real-world graphs often exhibit short average path lengths, meaning that the average path length is less than would be expected in a random graph. …