Measure community quality by attribute importance and density in social networks

Traditional community detection methods focused on the corresponding graph structure of social networks. Along with the advance on internet technology, especially online social networks, information besides network topology, such as node attributes, can be collected; such social networks are generally called attributed social networks (ASN). Therefore, recently, together with network topology such additional information is used to discover communities with better interpretation. However, definitions on a good community still vary from approach to approach. We assume that a good community in ASN should have strong attributes interactions besides of tense structural relation. Structural connections measures have been investigated for several decades, such as modularity. So, measuring attribute interactions is essential and urgent. We propose to measure attributes connections based on three factors: 1) global importance, 2) local importance, and 3) attribute density. By calculating such attributes closeness we can find potential communities that may have poor structural connection but strong attributes connections. We show the new measure effective through demonstration on some well known synthetic and real social networks.