The Role of Groups as Nodes in Networks

About this argument I found important things by a web-searching.

I write here what I learned about my research... ;)

A network consists of nodes connected by directed or undirected links. It is used to represent complex, relational data such as web pages or social networks. The nodes can be assigned roles, which are subjective characterization of the part they play in the network. For example, within the web, an authoritative page is one that is referred to by many other pages whereas a hub page is one that has hyperlinks to many other pages. There are a number of metrics that can be used to determine the roles of individual nodes in a network. Among those most widely used are degree, closeness, betweenness, and rank.

Knowledge of the node role (popularity, centrality, authority) is useful for many link mining applications such as Web search, threat detection, and co-citation analysis. Network community refers to groups of nodes that share similar properties. Despite its importance, none of the metrics that are used to define node roles explicitly use the community concept. Knowing the role that a node assumes with respect to its related communities would be a new and valuable tool for analysts. For example, in threat detection and crime analysis, knowing that a person has contacts with many groups could be valuable information

The problem of influence maximization can be thought of as finding the best k people to target in order to maximize the number of people that will eventually be influenced. Links are assigned a weight between 0 and 1 representing the probability that one node influences another when it is activated. Several algorithms have been developed in recent years to identify the most promising set of nodes to activate. These algorithms however focus only on maximizing the number of activated nodes at the end of the influence diffusion process. In some cases, it may be more useful to maximize the number of communities that are influenced.

A regular network is one where all of the nodes have a link to a fixed number of other nodes. A random network is one where the links between the nodes are completely random. Small world networks are somewhere between regular and random networks. They are characterized by many small groups of tightly connected nodes (like regular networks) with a few random links that connect the small groups (like random networks). Because of this, small world networks have the property that every two nodes are connected by a relatively short path.

Role is a concept that is used to describe the behavior of a node in relationship to its neighbors and to the networkat large. The discipline of social network analysis contains several centrality measures used to determine the roles of nodes in a network

An assumption of networks is that there are communities of nodes which are not explicitly exposed but that the links infer. In social networks we think of friends, family, and colleagues as forming communities.

The community-based node role is identified based on which of the four quadrants a node falls into. Community-based roles can be useful in a number of ways. Just by themselves these roles can provide useful information to analysts in areas as such as anti-terrorism and law enforcement. In searching for potential terrorist threats, for example, analysts may find it useful to concentrate on suspects with certain roles. If they were looking for persons with few friends but having diverse contacts they could focus on bridges. Community-based roles could also be utilized in existing techniques. The area of link mining has a number of techniques that use the relationships between objects to rank objects, select influential nodes, find communities as well other tasks. Many of them could potentially benefit from knowledge of the objects’ community role.