Node similarity is a fundamental problem in graph analytics. However, node similarity between nodes in different graphs (inter-graph nodes) has not received a lot of attention yet. The inter-graph node similarity is important in learning a new graph based on the knowledge of an existing graph (transfer learning on graphs) and has applications in biological, communication, and social networks. In this paper, we propose a novel distance function for measuring inter-graph node similarity with edit distance, called NED. In NED, two nodes are compared according to their local neighborhood structures which are represented as unordered k-adjacent trees, without relying on labels or other assumptions. Since the computation problem of tree edit distance on unordered trees is NP-Complete, we propose a modified tree edit distance, called TED*, for comparing neighborhood trees. TED* is a metric distance, as the original tree edit distance, but more importantly, TED* is polynomially computable. As a metric distance, NED admits efficient indexing, provides interpretable results, and shows to perform better than existing approaches on a number of data analysis tasks, including graph de-anonymization. Finally, the efficiency and effectiveness of NED are empirically demonstrated using real-world graphs.
To compare inter-graph nodes, neighborhood-based similarities have been used. Some primitive methods directly compare the ego-nets (direct neighbors) of two nodes using Jaccard coefficient, S rensen -- Dice coefficient, or Ochiai coefficient @cite_13 @cite_7 @cite_19 . Ness @cite_20 and NeMa @cite_27 expand on this idea and they use the structure of the @math -hop neighborhood of each node. However, for all these methods, if two nodes do not share common neighbors (or neighbors with the same labels), the distance will always be @math , even if the neighborhoods are isomorphic to each other.
@cite_7 @cite_19 @cite_27 @cite_13 @cite_20
2005207065 2134008243 1509240356 2017099446 2020657191
A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles. Network clustering (or graph partitioning) is an important task for the discovery of underlying structures in networks. Many algorithms find clusters by maximizing the number of intra-cluster edges. While such algorithms find useful and interesting structures, they tend to fail to identify and isolate two kinds of vertices that play special roles - vertices that bridge clusters (hubs) and vertices that are marginally connected to clusters (outliers). Identifying hubs is useful for applications such as viral marketing and epidemiology since hubs are responsible for spreading ideas or disease. In contrast, outliers have little or no influence, and may be isolated as noise in the data. In this paper, we proposed a novel algorithm called SCAN (Structural Clustering Algorithm for Networks), which detects clusters, hubs and outliers in networks. It clusters vertices based on a structural similarity measure. The algorithm is fast and efficient, visiting each vertex only once. An empirical evaluation of the method using both synthetic and real datasets demonstrates superior performance over other methods such as the modularity-based algorithms. It is increasingly common to find real-life data represented as networks of labeled, heterogeneous entities. To query these networks, one often needs to identify the matches of a given query graph in a (typically large) network modeled as a target graph. Due to noise and the lack of fixed schema in the target graph, the query graph can substantially differ from its matches in the target graph in both structure and node labels, thus bringing challenges to the graph querying tasks. In this paper, we propose NeMa (Network Match), a neighborhood-based subgraph matching technique for querying real-life networks. (1) To measure the quality of the match, we propose a novel subgraph matching cost metric that aggregates the costs of matching individual nodes, and unifies both structure and node label similarities. (2) Based on the metric, we formulate the minimum cost subgraph matching problem. Given a query graph and a target graph, the problem is to identify the (top-k) matches of the query graph with minimum costs in the target graph. We show that the problem is NP-hard, and also hard to approximate. (3) We propose a heuristic algorithm for solving the problem based on an inference model. In addition, we propose optimization techniques to improve the efficiency of our method. (4) We empirically verify that NeMa is both effective and efficient compared to the keyword search and various state-of-the-art graph querying techniques. The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a ‘functorial’ mapping of the original pattern. Such a mapping (essentially a generalized homomorphism) allows systematically for concatenation of effects through the network. The notion of functorial mapping is of central importance in the ‘theory of categories,’ a branch of modern algebra with numerous applications to algebra, topology, logic. The paper contains analyses of two social networks, exemplifying this approach. Complex social and information network search becomes important with a variety of applications. In the core of these applications, lies a common and critical problem: Given a labeled network and a query graph, how to efficiently search the query graph in the target network. The presence of noise and the incomplete knowledge about the structure and content of the target network make it unrealistic to find an exact match. Rather, it is more appealing to find the top-k approximate matches. In this paper, we propose a neighborhood-based similarity measure that could avoid costly graph isomorphism and edit distance computation. Under this new measure, we prove that subgraph similarity search is NP hard, while graph similarity match is polynomial. By studying the principles behind this measure, we found an information propagation model that is able to convert a large network into a set of multidimensional vectors, where sophisticated indexing and similarity search algorithms are available. The proposed method, called Ness (Neighborhood Based Similarity Search), is appropriate for graphs with low automorphism and high noise, which are common in many social and information networks. Ness is not only efficient, but also robust against structural noise and information loss. Empirical results show that it can quickly and accurately find high-quality matches in large networks, with negligible cost.