As Internet users interacting with their different friends in different social networks, the de-anonymization problem has been raising improving concern. Since the assailants may de-anonymize a social network by matching it with a correlated sanitized network and identifying anonymized user identities, multifarious arts study on the theoretical conditions or practical algorithms for correctly de-anonymizing a social network. Except for the structural information of these social networks, there has also been bounteous works taking advantage of some pre-identified seed nodes for reference in the anonymized network. In this paper, we systematically probe the theoretical conditions and algorithmic approaches for correctly matching two different-sized social networks by leveraging the multi-hop neighborhood relationships. A limited number of seeds are also taken into consideration as auxiliary information. To this end, we introduce the de-anonymization problem with the aid of the collectiveness and the collective adjacency disagreements, which are the collection of disagreements of different multi-hop adjacency matrices. We theoretically demonstrate that minimizing the collective adjacency disagreements can help match two social networks even in a very sparse circumstance, as it significantly enlarges the difference between the mismatched node pairs and the correctly matched pairs. Besides, the seeds is proved to bring positive influence in improving the de-anonymization accuracy. Algorithmically, we relax the domain of the matching function to continuum and adopt the conditional gradient descending method on the collective-form objective, to efficiently minimize the collective adjacency disagreements of two networks. We conduct tremendous experiments on different networks with or without seeds, the results of which return desirable de-anonymization accuracies and reveal the advantages of the collectiveness: the collectiveness manifests rich structural information, thereby most nodes can be correctly matched with their correspondences even in some sparse networks, where merely utilizing the 1-hop adjacency relationships might fail to work.