## 1 Introduction  
Mobile Opportunistic Networks (MONs) can be formed by wireless portable devices such as iPads, PDAs, smartphones, etc., which are usually carried around by human beings. Due to the random mobility of nodes, there are no persistent connections between any two nodes. For data transmission, each node stores data to be sent and then forwards them to the encounter nodes. Such a data delivery process refers to the \"storage-carry-and-forward\" mechanism, which is the basic principle for data transmission and routing in MONs. Since the path from a source to a destination is intermittently connected, the conventional routing protocols are generally not applicable, and routing becomes a challenging issue in MONs [1]. Based on the \"storage-carry-and-forward\" data transmission mode, two simple algorithms were proposed in the research on opportunistic routing. One is Epidemic Routing [2], and the other is DirectTransmission [3]. In Epidemic Routing, each node simply forwards data to all encountering nodes. Obviously, Epidemic Routing has the highest data delivery success rate among all routing algorithms but also has the highest network overhead. On the contrary, in Direct Transmission, the source node stores the data to be sent and does not forward them to any nodes until it reaches the destination. Direct Transmission had the lowest network overhead but also the lowest data delivery success rate. The other research works on routing in MONs tried to create a possible tradeoff between data delivery rate and network overhead. As human beings take part in network activities, the behavior of mobile nodes thus shows certain social attributes. Some research works [4] had shown that social relationships among nodes had an important impact on node encounter events and their duration time, which would be useful for reducing routing overhead improving the success rate of data transmission. Accordingly, a number of researchers made good use of nodes' social attributes to design data forwarding mechanisms and received good results. In the long run, the data transfer mechanism based on social relationships among nodes will be more stable than the other forwarding modes [4]. In social based routing, the key point is to find and measure the social relationships among nodes, which depend on the analysis of the historical data of encounters of nodes [5; 6]. Some works used historical data to predict the probability of the nodes' encounters, and thereby designed optimal algorithms for message forwarding. Some works measured strength of social relationships among nodes based on nodes' encounter frequency, formed social clusters of nodes, and proposed cluster-based routing mechanism for message forwarding. However, as for social relationship finding and measurement, there are still some important points not considered in the existing research work. For example, there is such a social phenomenon in the real world: [PERSON] has two grandmothers represented by \(D\) and \(E\), \(D\) is the mother of [PERSON]'s mother, and \(E\) is the mother of [PERSON]'s father. Although \(D\) and \(E\) are close relatives, they may never contact each other because of their opposing personalities. In this phenomenon, with \(D\) and \(E\) acting as two nodes in MONs, they have no direct encounter and link, but, in fact, there is a strong social relationship between them. Therefore, in some conditions, we may fail to find and measure the social relationship between two nodes only from their direct encounter records. In fact, although \(D\) and \(E\) have no direct relationship, they have common close friends including [PERSON] and his parents. Observing their circles of friends, we can find out how close the social relationship between \(D\) and \(E\) is. Consequently, the social relationship between two nodes can be divided into two parts. One part comes from direct contact events, which are called Explicit Social Relationships in this paper. Another part is called Implicit Social Relationships obtained from the common friends of the two nodes.