Keywords

Dynamic network, stable relational patterns, persistent, external factors, cliques, clustering etc. 
INTRODUCTION

Dynamic networks are generally modelled through a sequence of timebased graphs. Consecutive snapshots of the network at given intervals are also used. Entities, or nodes, in the network are connected via edges, or links which are also called as relations. Most reallife networks are dynamic in nature because they constantly add and remove nodes and links over time. Because of its flexibility and availability of theoretical and applied tools for efficient analysis dynamic networks have been used as generic model to represent the relations between various entities in diverse applications and to capture the temporal changes and dynamic aspects of the underlying data,. Examples of some widely used networks include the popular social networking sites like Facebook, the email network and biological networks [1].Graphs are considered as the universaldata structure to model entities and their relationships because all common data structures, vectors, strings and time series, can be represented as graphs. So, the amount of graphstructured data is ever increasing in a wide range of application domains such as bioinformatics, medicine, large database management and web log analysis. 
There is evolution in the amount and variety of data due to storage and exchange of lot of information in various applications. The majority of recent subgraph mining approaches have dedicated on characterizing the topology of static networks. But to model realworld systems, often a temporal component has to be taken into account, as relations between objects here usually occur for a certain period of time only. Therefore, a practical model has to consider that edges will be inserted and/or deleted over time. A new data structure is resulted which is called as a dynamic graph. Dynamic networks are flexible to capture the temporal changes and represent relations between entities in these applications. Numbers of tools are available in dynamic network for efficient analysis. This analysis of networks can provide significant insight about the stable relational patterns and their evolution over time. 
BACKGROUND

As we see everythingaround us is connected in some way, forming links, connections, or edges in some theoretical graph. Over the past years many algorithms have been discovered that helps to extract facts out of graphs. Graph pattern mining finds remarkable paths, trees, subgraphs, frequent induced subgraphs [5], and cliques within graph datasets.The information gained from graphs has been useful to solve many challenges in diverse domains such as computational biology, chemical informatics, and communications in networks. Frequent induced subgraph mining is used in the bioinformatics application domain to detect sets of functionally equivalent genetic factor [3]. Tree pattern mining can find out commonly occurring subtrees in a chemical compound dataset. Web access linkpath patterns enable internet service providers to predict frequently accessed resources that should be cached. Besides pattern mining, clustering is another usual data mining technique that has been applied to graphs. In the social graph, clustering has been used to identify highly consistent distinct groups, e.g. communities. In the chemical and bioinformatics domains, clustering has proven quite useful in the drug discovery process. Clustering is often applied for grouping datasets where the items are graphs, rather than nodes in a large graph. 
Most graph mining algorithms are based on the familiar association rule mining, or the frequent itemset problem. Frequent itemset mining algorithms are generally based on the lattice or downward closure property of support. This propertystates that an itemset cannot be frequent if even one of its subsets is not frequent. Frequent itemset mining algorithms specify all frequent itemsets by effectively pruning the search area. In terms of graph mining, downward closure translates to the fact that a subgraph is frequent only if all of its subgraphs are frequent. Most existing graph mining algorithms generalize up to date frequent itemset mining algorithms to structured data. 
LITERATURE SURVEY

Kuramochi, M., Karypis, G.

“Over the years, frequent item set discovery algorithms have been used to find interesting patterns in various application areas. However, as data mining techniques are being increasingly applied to nontraditional domains, existing frequent pattern discovery approaches cannot be used. This is because the transaction framework that is assumed by these algorithms cannot be used to effectively model the data sets in these domains. An alternate way of modeling the objects in these data sets is to represent those using graphs. Within that model, one way of formulating the frequent pattern discovery problem is that of discovering sub graphs that occur frequently over the entire set of graphs. They present a computationally efficient algorithm, called FSG, for finding all frequent sub graphs in large graph data sets. They experimentally evaluate the performance of FSG using a variety of real and synthetic data sets. Our results show that despite the underlying complexity associated with frequent sub graph discovery, FSG is effective in finding all frequently occurring sub graphs in data sets containing more than 200,000 graph transactions and scales linearly with respect to the size of the data set.” 
A. Chapanond, M. S. Krishnamoorthy, and B. Yener

“Analysis of social networks to identify communities and model their evolution has been an active area of recent research. This paper analyzes the Enron email data set to discover structures within the organization. The analysis is based on constructing an email graph and studying its properties with both graph theoretical and spectral analysis techniques. The graph theoretical analysis includes the computation of several graph metrics such as degree distribution, average distance ratio, clustering coefficient and compactness over the email graph. The spectral analysis shows that the email adjacency matrix has a rank2 approximation. It is shown that preprocessing of data has significant impact on the results, thus a standard form is needed for establishing a benchmark data.” 
L. Cerf, T. Nguyen, and J. Boulicaut

“Several algorithms, namely Cumbeminern, Trias, and DataPeeler, have been recently proposed to mine closed patterns in ternary relations. They consider here the specific context where a ternary relation denotes the value of a graph adjacency matrix at different timestamps. Then, we discuss the constraintbased extraction of patterns in such dynamic graphs. We formalize the concept of δcontiguous closed 3clique and we discuss the availability of a complete algorithm for mining them. It is based on a specialization of the enumeration strategy implemented in Data Peeler. Indeed, clique relevancy can be specified by means of a conjunction of constraints which can be efficiently exploited. The addedvalue of our strategy is assessed on a real dataset about a public bicycle renting system. The raw data encode the relationships between the renting stations during one year. The extracted δcontiguous closed 3cliques are shown to be consistent with our domain knowledge on the considered city.” 
J. Pei, J. Han, B. MortazaviAsl, H. Pinto, Q. Chen, U. Dayal, and M. Hsu

“Sequential pattern mining is an important data mining problem with broad applications. It is challenging since one may need to examine a combinatorially explosive number of possible subsequence patterns. Most of the previously developed sequential pattern mining methods follow the methodology of Apriori which may substantially reduce the number of combinations to be examined. However, Apriori still encounters problems when a sequence database is large and/or when sequential patterns to be mined are numerous and/or long. In this paper, theye propose a novel sequential pattern mining method, called Prefix Span (i.e., Prefixprojected Sequential pattern mining), which explores prefix projection in sequential pattern mining. Prefix Span mines the complete set of patterns but greatly reduces the efforts of candidate subsequence generation. Moreover, prefixprojection substantially reduces the size of projected databases and leads to efficient processing. Their performance study shows that Prefix Span outperforms both the Aprioribased GSP algorithm and another recently proposed method, Free Span, in mining large sequence databases.” 
B. Wackersreuther, P. Wackersreuther, A. Oswald, C. B. ohm, and K. Borgwardt

“In many application domains, graphs are utilized to model entities and their relationships, and graph mining is important to detect patterns within these relationships. While the majority of recent data mining techniques deal with static graphs that do not change over time, recent years have witnessed the advent of an increasing number of time series of graphs. In this paper, they define a novel framework to perform frequent subgraph discovery in dynamic networks. In particular, we are considering dynamic graphs with edge insertions and edge deletions over time. Existing subgraph mining algorithms can be easily integrated into our framework to make them handle dynamic graphs. Finally, an extensive experimental evaluation on a large realworld case study confirms the practical feasibility of our approach.” 
ALGORITHMS

Dynamic graphs are used to represent relationships between entities that evolve over time. Meaningful patterns in such structured data must capture strong interactions as well as their evolution over time. In social networks, such patterns can be seen as dynamic community structures, i.e., sets of individuals who strongly and repeatedly interact with each other. 
Constraintbased mining approach:

In this approach the temporal evolution of patterns is captured by associating a temporal event type to each identified subgraph to uncover evolving patterns [2]. This uses a new algorithm that finds such subgraphs in a time series of graphs incrementally. This considers the evolvingpattern mining problem in dynamic graph and presents five new pattern types which rely on two things: first, the extraction of dense subgraphs and second, the identification of their evolution. Five basic temporal events used are: The formation, termination, growth, reduction and stability of subgraphs from one time stamp to the next. 
This task is divided into a localtoglobal framework: Local patterns are first mined in a static graph; then they are combined with the one extracted in the previous graph to form evolving patterns. These patterns are defined by means of constraints that are used by the algorithm EVOLVINGSUBGRAPHS. In this way it efficiently mines all evolving patterns that satisfy the constraints.Constraintbased mining algorithms have advantage of the constraints to prune huge parts of the search space which cannot contain valid patterns. 
DFS Algorithm:

In many applications, graph mining is important to detect patterns within the relationships. While the majority of recent data mining techniques deal with static graphs that do not change over time. Now days there is increasing number of time series of graphs. A novel framework is presented to perform frequent subgraph discovery in dynamic networks[4]. 
Dynamic frequent subgraphdiscovery can be performed in two steps. First algorithms for finding frequent subgraphs in the union graph of a time series of graphs is used. Second the resulting static frequent subgraphs for frequent dynamic patterns are searched. DFS algorithm is used which provides a canonical representation based on sparse adjacency list data structure and implements a breadthfirst enumeration algorithm for discovering frequent subgraphs in dynamic network. It mainly considers dynamic graphs with edge insertions and edge deletions over time. 
Graphbased relational mining approach:

A new dynamic graphbased relational mining approach has been also developed to learn structural patterns in biological networks as they change over time [6]. The analysis of dynamic networks is important not only to understand life at the systemlevel, but also to discover original patterns in other structural data. Most current graphbased data mining approaches focus on only static graphs. This approach analyses a sequence of graphs and discovers rules that capture the changes that occur between pairs of graphs in the sequence and helps to understand how the biosystems change over time. Two step algorithm is used: Learning Graph Rewriting Rules and Learning Transformation Rules. First algorithm learns graph rewriting rules in a dynamic graphand represent how two sequential graphs are different. Second algorithm learns the repeated transformation rules in thelearned graph rewriting rules and describes how the graphchanges over time, where the changes are actually represented as a sequence of revised graphs. For both algorithms a previously developed method for finding thebest compressing subgraph in a set of graphs is used. For the firstalgorithm, repeated application of this method allows tofind the set of all subgraphs common to a pair of consecutivegraphs. For the second algorithm this method allows tofind the subgraphs repeatedly added and removed in the dynamic graph. A frequent subgraph miner is used for this purpose. As the quality and quantity of network and interaction data increases rapidly, the problem of effectively analyzing this data becomes significant. We can understand biological processes at a modular level by providing a framework for understanding cellular organization, functional hierarchy, and evolutionary conservation and using molecular interaction data. 
MULE Algorithm: 
Also an innovative new algorithm, Mining UniqueLabeledEdgesets (MULE) is used for detecting frequently occurring patterns and modules in biological networks [10]. The algorithm considers the problems computationally tractable and scalable to large numbers of networks by using an innovative graph simplification technique which is based on ortholog contraction, ideally suited to biological networks. MULE is based on frequent itemset extraction to discover frequent subgraphs among the graphs. It takes into account the nature of molecular interaction data. Existing formulations of isomorphism based frequent subgraph extraction suffer from exponential explosion of problem size due to NPhardness of both mining and subgraph isomorphism problems. In contrast to such extant approaches, MULE avoids the repeated solution of NPhard subgraph isomorphism problem and also preserves the biological relevance of identified patterns. This algorithm makes use of a recursive subroutine to extend frequent edgesets. 
Finding periodic or near periodic subgraph:

It is infrequent and hard to detect interaction patterns within a social network because social interactions occur regularly. To identify such regular behavior, a new mining problem of finding periodic or near periodic subgraphs in dynamic social networks is used [8]. This analyzes the computational complexity of the problem, showing that, unlike any of the related subgraph mining problems, it is polynomial. A practical, efficient and scalable algorithm is used to find such subgraph that takes imperfect periodicity into account. An efficient, singlepass algorithm for mining all closed periodic subgraphs in a dynamic network is given. This algorithm is polynomial time and space algorithm. 
The basis of the algorithm is a pattern tree. This pattern tree maintains information about all patterns that are either currently periodic or could become periodic at a future timestamp. As each new timestamp is read, the pattern tree is traversed and updated with the information. Any patterns that are no longer periodic are flushed, and new periodic patterns are possibly created. The algorithm maintains two data structures: the pattern tree and a subgraph hash map. 
There are some disadvantages of existing techniques such as follows: 
1. The existing techniques can only detect the frequent patterns in a dynamic network or follow related patterns over time. 
2. They are not designed to identify stable relational patterns. 
3. They do not focus on tracking the changes of preserved relational patterns over time. 
Applications of stable pattern mining are as follows: 
1. It is useful in mining biochemical structures. 
2. Program control flow analysis can be determined using stable pattern mining. 
3. Mining XML structures or Web communities is also possible. 
4. Social networking sites, email networks can be analyzed. 
CONCLUSION AND FUTURE WORK

This paper gives an overview of the methods used in the mining of stable relational patterns in dynamic networks. It also compares methods based on static graph mining with those using the time component in the network. In many cases, both types of algorithms resulted in similar time complexity. Many newer algorithms appear to build upon older algorithms in dynamic network mining. Two things that helped in producing effective algorithms for certain mining tasks were the use of certain data structures to speed up operations and extreme pruning of the search space. We can also determine conserved relational states in dynamic network to understand change of entity from one state to another state. 

Tables at a glance


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