Graph Search & Social Networks Shuai Ma Graphs are everywhere, and quite a few are huge graphs! 2 Application Scenarios Software plagiarism detection [1] • Traditional plagiarism detection tools may not be applicable for serious software plagiarism problems. • A new tool based on graph pattern matching – Represent the source codes as program dependence graphs [2]. – Use graph pattern matching to detect plagiarism. 3 Application Scenarios Recommender systems [3] • Recommendations have found its usage in many emerging specific applications, such as social matching systems. • Graph search is a useful tool for recommendations. – A headhunter wants to find a biologist (Bio) to help a group of software engineers (SEs) analyze genetic data. – To do this, (s)he uses an expertise recommendation network G, as depicted in G, where a node denotes a person labeled with expertise, and an edge indicates recommendation, e.g., HR1 recommends Bio1, and AI1 recommends DM1 4 Application Scenarios Transport routing [4] • Graph search is a common practice in transportation networks, due to the wide application of Location-Based Services. • Example: Mark, a driver in the U.S. who wants to go from Irvine to Riverside in California. – If Mark wants to reach Riverside by his car in the shortest time, the problem can be expressed as the shortest path problem. Then by using existing methods, we can get the shortest path from Irvine, CA to Riverside, CA traveling along State Route 261. – If Mark drives a truck delivering hazardous materials may not be allowed to cross over some bridges or railroad crossings. This time we can use a pattern graph containing specific route constraints (such as regular expressions) to find the optimal transport routes. 5 Application Scenarios Biological data analysis [5] • A large amount of biological data can be represented by graphs, and it is significant to analyze biological data with graph search techniques. – “Protein-interaction network (PIN) analysis provides valuable insight into an organism’s functional organization and evolutionary behavior.” – For example, one can get the topological properties of a PIN formed by highconfidence human protein interactions obtained from various public interaction databases by PIN analysis. 6 Outline • • • • • What is graph search? Graph search, why bother? Three Types of Graph Search Challenges & Related techniques Summary 7 What is Graph Search? 8 What is Graph Search? A unified definition [6] (in the name of graph matching): • Given a pattern graph Gp and a data graph G: – check whether Gp ‘‘matches’’ G; and – identify all ‘‘matched’’ subgraphs. Remarks: – Two classes of queries: – Boolean queries (Yes or No) – Functional queries, which may use Boolean queries as a subroutine – Graphs contain a set of nodes and a set of edges, typically with labels – Pattern graphs are typically small (e.g., 10), but data graphs are usually huge (e.g., 108) 9 What is Graph Search? Different semantics of “match” implies different “types” of graph search, including, but not limited to, the following: • • • • • • • Shortest paths/distances[4] Subgraph isomorphism[12] Graph homomorphism and its extensions[10] Graph simulation and its extensions[8,9] Graph keyword search[7] Neighborhood queries[11] … Graph search is a very general concept! 10 Graph Search, Why Bother? Social Networks are the New Media Social networks are graphs • The nodes are the people and groups • The links/edges show relationships or flows between the nodes. 12 Social Networks are the New Media Social networks are becoming an important way to get information in everyday life！ 13 The need for a Social Search Engine File systems Databases World Wide Web Social Networks • File systems - 1960’s： very simple search functionalities • Databases - mid 1960’s：SQL language • World Wide Web - 1990’s：keyword search engines • Social networks - late 1990’s: Facebook launched “graph search” on 16th January, 2013 Assault on Google, Yelp, and LinkedIn with new graph search; Yelp was down more than 7% Graph search is a new paradigm for social computing! 14 Graph Search vs. RDBMS [13] Query： Find the name of all of Alberto Pepe's friends. Step 1: The person.name index -> the identifier of Alberto Pepe. [O(log2n)] Step 2: The friend.person index -> k friend identifiers. [O(log2x) : x<<m] Step 3: The k friend identifiers [O(k log2n)] -> k friend names. 15 Graph Search vs. RDBMS [13] Query： Find the name of all of Alberto Pepe's friends. Step 1: The vertex.name index -> the vertex with the name Alberto Pepe. [O(log2n)] Step 2: The vertex returned -> the k friend names. [O(k + x)] 16 Social Search vs. Web Search • Phrases、short sentences vs. key words only • (Simple Web) pages vs. Entities • Lifeless vs. Full of life • History vs. Future it’s interesting, and over the last 10 years, people have been trained on how to use search engines more effectively. Keywords & Search In 2013: Interview With A. Goodman & M. Wagner International Conference on Application of Natural Language to Information Systems (NLDB) started from 1995 Interesting Coincidence! SIGMOD + VLDB + ICDE 40 35 30 25 20 15 10 5 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Social computing & Web 2.0 DB people started working on graphs at around the same time！ 18 Three Types of Graph Search • Cohesive subgraphs • Keyword search on graphs • Graph pattern matching 19 Cohesive Subgraphs • Cohesive subgroups are subsets of actors among whom there are relatively strong, direct, intense, frequent or positive ties [14]. – Different cohesive subgroups are formed according to different cohesive relations, which are further specified by application needs. • Social networks can be represented as graphs, such that we formalize cohesive subgroups as cohesive subgraphs. – Correspondingly, the problem of finding cohesive subgraphs on graphs are referred to as Cohesive subgraph search. 20 Cohesive Subgraphs • Various cohesive subgraphs (clique, n-clan, k-plex, k-core) Maximal clique: a maximal clique is a maximal complete subgraph. • Main issues: – Cliques can overlap – Too many or too few cliques emerge – The problem is NP-complete “Padgett's Florentine Families” 21 Cohesive Subgraphs • Various cohesive subgraphs (clique, n-clan, k-plex, k-core) N-clique: an n-clique is a maximal subgraph in which the largest distance between any two nodes is no greater than n. N-clan: an n-clan is an n-clique in which the diameter is no greater than n. K-core: a k-core is a maximal subgraph in which the nodal degree of each node is no smaller than k. “Padgett's Florentine Families” The cohesive relations are gradually looser 22 Keyword Search on Graphs • Given a set of keywords and a data graph, the problem is to determine a group of densely linked nodes in the graph such that the nodes together – contain all the keywords, and – satisfy some structural constrains [7] Remarks: 1. Different “structure constraints” implies different types of keyword search. 2. Keyword search is a very simple but user-friendly information retrieval mechanism. 23 Keyword Search on Graphs Given keywords: {A, B} Minimum spanning tree [7] 5 : {B, G} 1 : {B} 4 : {A} 2 : {C, E} 6 : {A, E} 3 : {D} 7 : {D, F} 24 Keyword Search on Graphs r-clique [15] 5 : {B, G} 1 : {B} 4 : {A} 2 : {C, E} 6 : {A, E} 3 : {D} 7 : {D, F} Lack of input structure constrains, the results requires ranking Lack justification of the usage of the structure constrains 25 Graph Pattern Matching [17] • Given two directed graphs G1 (pattern graph) and G2 (data graph), – decide whether G1 “matches” G2 (Boolean queries); – identify “subgraphs” of G2 that match G1 • Matching Semantics – Traditional: Subgraph Isomorphism – Emerging applications: Graph Simulation and its extensions, etc.. 26 Subgraph Isomorphism[12] • Given Pattern graph Q, subgraph Gs of data graph G – Q matches Gs if there exists a bijective function f: VQ→ VGs such that for each node u in Q, u and f(u) have the same label An edge (u, u‘) in Q if and only if (f(u), f(u')) is an edge in Gs • Goodness: Keep exact structure topology between Q and Gs • Badness: Decision problem is NP-complete May return exponential many matched subgraphs In certain scenarios, too restrictive to find matches These hinder the usability in emerging applications, e.g., social networks 27 Graph Simulation • Given pattern graph Q(Vq, Eq) and data graph G(V, E), a binary relation R ⊆ Vq × V is said to be a match if – (1) for each (u, v) ∈ R, u and v have the same label; and – (2) for each edge (u, u′) ∈ Eq, there exists an edge (v, v′) in E such that (u′, v′) ∈ R. • Graph G matches pattern Q via graph simulation, if there exists a total match relation M – for each u ∈ Vq, there exists v ∈ V such that (u, v) ∈ M. – Intuitively, simulation preserves the labels and the child relationship of a graph pattern in its match. – Simulation was initially proposed for the analyses of programs; and simulation and its extensions were recently introduced for social networks. Subgraph isomorphism (NP-complete) vs. graph simulation (O(n2))! 28 Subgraph Isomorphism Set up a team to develop a new software product Graph simulation returns F3, F4 and F5; Subgraph isomorphism returns empty! Subgraph isomorphism is too strict for emerging applications 29 Terrorist Collaboration Network “Those who were trained to fly didn’t know the others. One group of people did not know the other group.” (Osama Bin Laden, 2001) 30 Strong Simulation[16,17] • Subgraph isomorphism – Goodness Keep (strong) structure topology – Badness May return exponential number of matched subgraphs Decision problem: NP-complete In certain scenarios, too restrictive to find sensible matches • Graph simulation – Goodness Solvable in quadratic time – Badness Lose structure topology (how much? open question) Only return a single matched subgraph Balance between complexity and the capability to capturing topology! 31 Strong Simulation Disconnected • Graph simulation loses graph structures Tree Long cycle 32 Strong Simulation • Duality (dual simulation) – Both child and parent relationships – Simulation considers only child relationships • Locality – Restricting matches within a ball – When social distance increases, the closeness of relationships decreases and the relationships may become irrelevant • The semantics of strong simulation is well defined – The results are unique Strong simulation: bring duality and locality into graph simulation 33 Strong Simulation Subgraph Isomorphism Strong Simulation Dual Simulation Graph Simulation Topology preservation and bounded matches 34 Strong Simulation • A new matching model referred to as strong simulation • A cubic time algorithm • Three main optimization techniques – Query minimization An O(n2) algorithm – Dual simulation filtering First compute the match graph of dual simulation, then project on each ball of the data graph – Connectivity pruning Based on the connectivity theorem • A distributed algorithm – Data locality property – Boundary nodes and radius Towards revising conventional notions of graph matching 35 Analyses Graph search Userfriendliness Result-accuracy Cohesive Subgraphs Keyword Search Keywords Graph Pattern Matching Pattern graphs Result ranking More accurate (well structure constrained) A novel approach to combining the advantages and overcoming the shortcomings of existing graph search. 36 Challenges & Related techniques 37 Big Data • Big Data refers to datasets that grow so large that it is difficult to capture, store, manage, share, analyze and visualize with those traditional (database) software tools “Big data” has become a Buzz word, and the common focus of both industrial and academic communities! More Data Beats Better Algorithms Kepler's third law of planetary motion • The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit Social networks are “big data” Facebook: • • • • Volume： 10 x 108 users, 2400 x 108 photos, 104 x 108 page visits Velocity： 7.9 new users per second, over 60 thousands per day Variety： text (weibo, blogs) , figures, videos, relationships (topology) Value：1.5 x 108 dollars in 2007, 3 x 108 dollars in 2008, 6 ~ 7 x 108 dollars in 2009, 10 x 108 dollars in 2010. • Further, data are often dirty due to data missing and data uncertainty [18, 19] Challenges – The amount of data has reached hundred millions orders of magnitude. Graph search with high efficiency, striking a balance between its performance and accuracy. – The data are updated all the time, and the updated amount of data daily reaches hundred thousands orders of magnitude. Consider the dynamic changes and timing characteristics of data. – Same with traditional relational data, there exists data quality problems such as data uncertainty and data missing in the new applications. Solve the data quality problems. 42 Related Techniques 43 Distributed Processing • Real-life graphs are typically way too large: – Yahoo! web graph: 14 billion nodes – Facebook: over 0.8 billion users It is NOT practical to handle large graphs on single machines • Real-life graphs are naturally distributed: – Google, Yahoo! and Facebook have large-scale data centers Distributed graph processing is inevitable It is nature to study “distributed graph search”! 44 Distributed Processing Model of Computation [3]: • A cluster of identical machines (with one acted as coordinator); • Each machine can directly send arbitrary number of messages to another one; • All machines co-work with each other by local computations and message-passing. Complexity measures: 1. Visit times: the maximum visiting times of a machine (interactions) 2. Makespan: the evaluation completion time (efficiency) 3. Data shipment: the size of the total messages shipped among distinct machines (network band consumption) 45 Incremental Techniques Google Percolator [20]: • Converting the indexing system to an incremental system, • Reduce the average document processing latency by a factor of 100 • Process the same number of documents per day, while reducing the average age of documents in Google search results by 50%. It is a great waste to compute everything from scratch! 46 Data Preprocessing • Data sampling – Instead of dealing with the entire data graphs, it reduces the size of data graphs by sampling and allows a certain loss of precision. – In the sampling process, ensure that the sampling data obtained can reflect the characteristics and information of the original data graphs as much as possible. • Data compression – It generates small graphs from original data graphs that preserve the information only relevant to queries. – A specific compression method is applied to a specific query application, such that data graph compression is not universal for all query applications. – Reachability query, Neighbor query 47 Data Preprocessing • Indexing • There are mainly three standards for measuring the goodness of an indexing method. – The space of a graph index – Establishing time for a graph index – Query time with a graph index • Data partitioning – Partition a data graph to relatively “small” graphs – Hash function is a simple approach for random partitioning. – There are well established tools, e.g. Metis. 48 Summary 49 We have introduced graph search: a new paradigm for social computing We have discussed the history and applications of graph search We have introduced and analyzed three types of graph search： – Cohesive subgraphs – Keyword search on graphs – Graph pattern matching We have also discussed the challenges and related techniques We have presented some useful techniques to solve the problems 50 References [1] Chao Liu, Chen Chen, Jiawei Han and Philip S. Yu, GPLAG: detection of software plagiarism by program dependence graph analysis. KDD 2006. [2] J. Ferrante, K. J. Ottenstein, and J. D. Warren. The program dependence graph and its use in optimization. ACM Trans. Program. Lang. Syst., 9(3):319–349, 1987. [3] Shuai Ma, Yang Cao, Jinpeng Huai, and Tianyu Wo, Distributed Graph Pattern Matching, WWW 2012. [4] Rice, M. and Tsotras, V.J., Graph indexing of road networks for shortest path queries with label restrictions,VLDB 2010. [5] David A. Bader and Kamesh Madduri, A graph-theoretic analysis of the human proteininteraction network using multicore parallel algorithms. Parallel Computing 2008. [6] Shuai Ma, Yang Cao, Tianyu Wo, and Jinpeng Huai, Social Networks and Graph Matching. Communications of CCF, 2012. [7] C. C. Aggarwal and H. Wang. Managing and Mining Graph Data. Springer, 2010. [8] Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, and Yinghui Wu, Adding Regular Expressions to Graph Reachability and Pattern Queries. ICDE 2011. [9] Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, and Yinghui Wu, Graph Pattern Matching: From Intractable to Polynomial Time. VLDB 2010. [10] Wenfei Fan, Jianzhong Li, Shuai Ma, Nan Tang, and Yinghui Wu, Graph Homomorphism Revisited for Graph Matching. VLDB 2010. 51 References [11] Hossein Maserrat and Jian Pei, Neighbor query friendly compression of social networks. KDD 2010. [12] Brian Gallaghe, Matching structure and semantics: A survey on graph-based pattern matching. AAAI FS. 2006. [13] Marko A. Rodriguez, Peter Neubauer: The Graph Traversal Pattern. Graph Data Management 2011: 29-46 [14] S.Wasserman and K. Faust. Social Network Analysis: Methods and Applications. Cambridge University Press, 1994. [15] Mehdi Kargar, Aijun An: Keyword Search in Graphs: Finding r-cliques. In VLDB Conference, 2011. [16] Shuai Ma, Yang Cao, Wenfei Fan, Jinpeng Huai, and Tianyu Wo, Capturing Topology in Graph Pattern Matching. VLDB 2012. [17] Wenfei Fan, Graph Pattern Matching Revised for Social Network Analysis. ICDT 2012. [18] Eytan Adar and Christopher Re, Managing Uncertainty in Social Networks, IEEE Data Eng. Bull., pp.15-22, 30(2), 2007. [19] Gueorgi Kossinets, Effects of missing data in social networks. Social Networks 28:247268, 2006. [20] Daniel Peng, Frank Dabek: Large-scale Incremental Processing Using Distributed Transactions and Notifications. OSDI 2010. 52 Acknowledgement: Yang Cao, Wenfei Fan, Kaiyu Feng, Jinpeng Huai, Jia Li, Jianzhong Li, Xudong Liu, Nan Tang, Tianyu Wo, Yinghui Wu, … Homepage: http://mashuai.buaa.edu.cn Email: mashuai@buaa.edu.cn Address: Room G1122, New Main Building, Beihang University 53 Book Recommendation 54 Databases and Logic 55 Computational Complexity 56 Algorithms 57 Formal Languages 58 Statistics and Social Networks 59 Graph Theory 60 Thanks!

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