Extracting relationship information within social network using activity profiles

Abstract

When part of the information about a social network is missing, we hope to utilize the information we already have to extract the missing information. If we regard the actors as nodes and the relations between actors as edges, social networks can be represented by graphs. Thus, we can use graph theory techniques to solve some social network problems. This thesis discusses the construction processes of graphs based on two kinds of social networks problems and provides approaches for solving the problems.

2. A heuristic approach, which finds a matching in quadratic time.

1. An exact approach using the Blossom algorithm, which finds a maximum matching in cubic time.

After each complete message got broken into two halves in the first problem, the second problem in the thesis discusses a more difficult situation where the information about whether a half message is a sent half or a received half is missing. Hence, we cannot distinguish between sent half messages and received half messages, which means they all look the same to us. In this situation, a half message becomes an activation with an actor ID and an activation time. We want to rebuild the complete messages by pairing the activations. Therefore, we need to find a matching of the activations. The thesis provides two approaches for solving this problem:

2. A linear approximation algorithm approach, which finds a matching with an expected accuracy of at least 0.5 in linear time.

1. A dynamic programming algorithm approach, which finds a maximum matching in quadratic time.

Suppose in a messaging system, people can send messages to each other. Each complete message has a sender ID, a sending time, a receiver ID and a receiving time. The first problem in the thesis discusses a situation where somehow each complete message got broken into two half messages: a sent half message (with a sender ID and a sending time) and a received half message (with a receiver ID and a receiving time) and there is no link between them. At this point, instead of having a list of complete messages, we have a list of sent half messages and a list of received half messages with no link between them. Our goal is to rebuild the complete messages by pairing the sent and received half messages together. To achieve our goal, we need to find a bipartite matching between the sent half messages and the received half messages. The thesis provides two approaches for this problem: