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<!DOCTYPE html>
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<title>Neo4j Graph Algorithms</title>
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<body class="article toc2 toc-left">
<div id="header">
<h1>Neo4j Graph Algorithms</h1>
<div id="toc" class="toc2">
<div id="toctitle">Table of Contents</div>
<ul class="sectlevel1">
<li><a href="#_introduction">Introduction</a>
<ul class="sectlevel2">
<li><a href="#_algorithms">Algorithms</a></li>
<li><a href="#_installation">Installation</a></li>
<li><a href="#_usage">Usage</a></li>
<li><a href="#_building_locally">Building Locally</a></li>
</ul>
</li>
<li><a href="#_yelp">Yelp</a>
<ul class="sectlevel2">
<li><a href="#_yelp_open_dataset">Yelp Open Dataset</a></li>
<li><a href="#_data">Data</a></li>
<li><a href="#_graph_model">Graph Model</a></li>
<li><a href="#_import">Import</a></li>
<li><a href="#_networks">Networks</a></li>
</ul>
</li>
<li><a href="#_overview_of_algorithm_procedures">Overview of Algorithm Procedures</a></li>
<li><a href="#_algorithms_2">Algorithms</a>
<ul class="sectlevel2">
<li><a href="#_community_detection_triangle_counting_clustering_coefficient">Community detection: Triangle Counting / Clustering Coefficient</a></li>
<li><a href="#_page_rank">Page Rank</a></li>
<li><a href="#_betweenness_centrality">Betweenness Centrality</a></li>
<li><a href="#_closeness_centrality">Closeness Centrality</a></li>
<li><a href="#_minimum_weight_spanning_tree">Minimum Weight Spanning Tree</a></li>
<li><a href="#_all_pairs_and_single_source_shortest_path">All Pairs- and Single Source - Shortest Path</a></li>
<li><a href="#_graph_partitioning_label_propagation">Graph Partitioning: Label Propagation</a></li>
<li><a href="#_community_detection_connected_components">Community detection: Connected Components</a></li>
<li><a href="#_community_detection_strongly_connected_components">Community detection: Strongly Connected Components</a></li>
</ul>
</li>
<li><a href="#_implementers_section">Implementers Section</a>
<ul class="sectlevel2">
<li><a href="#_algorithm_procedures_api_discussion">Algorithm Procedures API Discussion</a></li>
<li><a href="#_api_documentation">API Documentation</a></li>
<li><a href="#_triangle_count">Triangle Count</a></li>
<li><a href="#_pagerank">PageRank</a></li>
<li><a href="#_betweenness_centrality_2">Betweenness Centrality</a></li>
<li><a href="#_closeness_centrality_2">Closeness Centrality</a></li>
<li><a href="#_minimum_weight_spanning_tree_2">Minimum Weight Spanning Tree</a></li>
<li><a href="#_single_shortest_path">Single Shortest Path</a></li>
<li><a href="#_label_propagation">Label Propagation</a></li>
<li><a href="#_weakly_connected_components">Weakly Connected Components</a></li>
<li><a href="#_strongly_connected_components">Strongly Connected Components</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="content">
<div class="sect1">
<h2 id="_introduction"><a class="link" href="#_introduction">Introduction</a></h2>
<div class="sectionbody">
<div class="paragraph">
<p>The goal of this library is to provide efficiently implemented, parallel versions of common graph algorithms for Neo4j 3.x exposed as Cypher procedures.</p>
</div>
<div class="paragraph">
<p>Releases are available here: <a href="https://github.com/neo4j-contrib/neo4j-graph-algorithms/releases" class="bare">https://github.com/neo4j-contrib/neo4j-graph-algorithms/releases</a></p>
</div>
<div class="sect2">
<h3 id="_algorithms"><a class="link" href="#_algorithms">Algorithms</a></h3>
<div class="paragraph">
<p>Centralities:</p>
</div>
<div class="ulist">
<ul>
<li>
<p>Page Rank (<code>algo.pageRank</code>)</p>
</li>
<li>
<p>Betweenness Centrality (<code>algo.betweenness</code>)</p>
</li>
<li>
<p>Closeness Centrality (<code>algo.closeness</code>)</p>
</li>
</ul>
</div>
<div class="paragraph">
<p>Community Detection:</p>
</div>
<div class="ulist">
<ul>
<li>
<p>Louvain (<code>algo.louvain</code>)</p>
</li>
<li>
<p>Label Propagation (<code>algo.labelPropagation</code>)</p>
</li>
<li>
<p>(Weakly) Connected Components (<code>algo.unionFind</code>)</p>
</li>
<li>
<p>Strongly Connected Components (<code>algo.scc</code>)</p>
</li>
<li>
<p>Triangle Count / Clustering Coefficient (<code>algo.triangleCount</code>)</p>
</li>
</ul>
</div>
<div class="paragraph">
<p>Path Finding:</p>
</div>
<div class="ulist">
<ul>
<li>
<p>Minimum Weight Spanning Tree (<code>algo.mst</code>)</p>
</li>
<li>
<p>All Pairs- and Single Source - Shortest Path (<code>algo.shortestPath</code>, <code>algo.allShortestPaths</code>)</p>
</li>
</ul>
</div>
<div class="paragraph">
<p>These procedures work either on the whole graph or on a subgraph optionally filtered by label and relationship-type.
You can also use filtering and projection using Cypher queries, see below.</p>
</div>
<div class="paragraph">
<p><strong>We’d love your feedback</strong>, so please try out these algorithms and let us know how well they work for your use-case.
Also please note things that you miss from installation instructions, documentation, etc.</p>
</div>
<div class="paragraph">
<p>Please raise <a href="https://github.com/neo4j-contrib/neo4j-graph-algorithms/issues">GitHub issues</a> for anything you encounter or join the <a href="http://neo4j.com/developer/slack">neo4j-users Slack group</a> and ask in the <code>#neo4j-graph-algorithm</code> channel.</p>
</div>
</div>
<div class="sect2">
<h3 id="_installation"><a class="link" href="#_installation">Installation</a></h3>
<div class="paragraph">
<p>Just copy the <code>graph-algorithms-algo-*.jar</code> from <a href="https://github.com/neo4j-contrib/neo4j-graph-algorithms/releases">the matching release</a> into your <code>$NEO4J_HOME/plugins</code> directory.</p>
</div>
<div class="paragraph">
<p>Because the algorithms use the lower level Kernel API to read from and write to Neo4j you also have to enable them in the configuration (for security reasons):</p>
</div>
<div class="listingblock">
<div class="title">Add to $NEO4J_HOME/conf/neo4j.conf</div>
<div class="content">
<pre>dbms.security.procedures.unrestricted=algo.*</pre>
</div>
</div>
<div class="paragraph">
<p>Then running <code>call algo.list();</code> should list the algorithm procedures.
You can also see the full list in the documentation.</p>
</div>
</div>
<div class="sect2">
<h3 id="_usage"><a class="link" href="#_usage">Usage</a></h3>
<div class="paragraph">
<p>These algorithms are exposed as Neo4j procedures.
You can call them directly from Cypher in your Neo4j Browser, from cypher-shell or your client code.</p>
</div>
<div class="paragraph">
<p>For most algorithms we provide two procedures, one that writes results back to the graph as node-properties and reports statistics.
And another (named <code>algo.<name>.stream</code>) that returns a stream of data, e.g. node-ids and computed values.</p>
</div>
<div class="paragraph">
<p>For large graphs the streaming procedure might return millions or billions of results, that’s why it is often more convenient to store the results of the algorithm and then use them with later queries.</p>
</div>
<div class="paragraph">
<p>The general call syntax is:</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-cypher" data-lang="cypher">CALL algo.<name>([label],[relationshipType],{config})</code></pre>
</div>
</div>
<div class="paragraph">
<p>For example for page rank on DBpedia (11M nodes, 116M relationships):</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-cypher" data-lang="cypher">CALL algo.pageRank('Page','Link',{iterations:5, dampingFactor:0.85, write: true, writeProperty:'pagerank'});
// YIELD nodes, iterations, loadMillis, computeMillis, writeMillis, dampingFactor, write, writeProperty
CALL algo.pageRank.stream('Page','Link',{iterations:5, dampingFactor:0.85})
YIELD node, score
RETURN node.title, score
ORDER BY score DESC LIMIT 10;</code></pre>
</div>
</div>
<div class="sect3">
<h4 id="_projection_via_cypher_queries"><a class="link" href="#_projection_via_cypher_queries">Projection via Cypher Queries</a></h4>
<div class="paragraph">
<p>If label and relationship-type are not selective enough to describe your subgraph to run the algorithm on, you can use Cypher statements to load or project subsets of your graph.
Then use a node-statement instead of the label parameter and a relationship-statement instead of the relationship-type and use <code>graph:'cypher'</code> in the config.</p>
</div>
<div class="paragraph">
<p>You can also return a property value or weight (according to your config) in addition to the id’s from these statements.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-cypher" data-lang="cypher">CALL algo.pageRank(
'MATCH (p:Page) RETURN id(p) as id',
'MATCH (p1:Page)-[:Link]->(p2:Page) RETURN id(p1) as source, id(p2) as target, count(*) as weight',
{graph:'cypher', iterations:5, write: true});</code></pre>
</div>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_building_locally"><a class="link" href="#_building_locally">Building Locally</a></h3>
<div class="paragraph">
<p>Currently aiming at Neo4j 3.x (with a branch per version)</p>
</div>
<div class="listingblock">
<div class="content">
<pre>git clone https://github.com/neo4j-contrib/neo4j-graph-algorithms
cd neo4j-graph-algorithms
git checkout 3.3
mvn clean install
cp algo/target/graph-algorithms-*.jar $NEO4J_HOME/plugins/
$NEO4J_HOME/bin/neo4j restart</pre>
</div>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_yelp"><a class="link" href="#_yelp">Yelp</a></h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_yelp_open_dataset"><a class="link" href="#_yelp_open_dataset">Yelp Open Dataset</a></h3>
<div class="paragraph">
<p><a href="https://www.yelp.com/">Yelp.com</a> has been running <a href="https://www.yelp.com/dataset/challenge">Yelp Dataset challenge</a> for about five years now.
It is a competition that encourages people to explore and research Yelp’s open dataset, which contains almost 5 million reviews from over 1.1 million users on over 150,000 businesses from 12 metropolitan areas in the tenth round of the challenge.
Over the years the dataset has become very popular with <a href="https://scholar.google.com/scholar?q=citation%3A+Yelp+Dataset&btnG=&hl=en&as_sdt=0%2C5">hundreds of academic paper</a> written about it.
It has well-structured and highly relational data and is therefore a great showcase for Neo4j and graph algorithms on a realistic dataset.
We will show how to use graph algorithms on a social network of friends and how to create and analyse an inferred graph (for example, projecting a review co-occurence graph or similarity between users based on their reviews).</p>
</div>
<div class="paragraph">
<p>Check out also <a href="https://www.yelp.com/dataset/challenge/winners">past winners and their work</a>.</p>
</div>
</div>
<div class="sect2">
<h3 id="_data"><a class="link" href="#_data">Data</a></h3>
<div class="paragraph">
<p>You can <a href="https://www.yelp.com/dataset/download">get the dataset</a> by filling out their form.
Download the data in JSON format.
We will use <a href="https://github.com/neo4j-contrib/neo4j-apoc-procedures/releases">APOC plugin</a> to help us with importing and batching data in Neo4j.
There are 6 JSON files available (<a href="https://www.yelp.com/dataset/documentation/json">detailed documentation</a>).
Photos and checkins are not the topic of our analysis, so they will not be imported.
From the other files we will import a knowledge graph of Yelp’s world, that contains data about:</p>
</div>
<div class="ulist">
<ul>
<li>
<p>156639 businesses</p>
</li>
<li>
<p>1005693 tips from users about businesses</p>
</li>
<li>
<p>4736897 reviews of businesses by users</p>
</li>
<li>
<p>9489337 users total</p>
</li>
<li>
<p>35444850 friend relationships</p>
</li>
</ul>
</div>
<div class="paragraph">
<p>Depending on your setup import might take some time as <em>user.json</em> contains data about a 10 million person social network of friends.
While <em>review.json</em> is even bigger in size, it is mostly made up of text representing the actual review, so the import will be faster.
We also do not need the actual text, but only meta-data about them e.g. who wrote the review and how he rated a certain business, so the text will not be imported.</p>
</div>
</div>
<div class="sect2">
<h3 id="_graph_model"><a class="link" href="#_graph_model">Graph Model</a></h3>
<div class="imageblock">
<div class="content">
<img src="https://github.com/neo4j-contrib/neo4j-graph-algorithms/raw/3.1/doc/img/yelp_graph_model.png" alt="yelp graph model">
</div>
</div>
<div class="paragraph">
<p>Graph consist of nodes labeled User, that can have a FRIEND relationship with other users. Users also write reviews and tips about businesses. We store all the meta-data ( location of business etc.) as properties of nodes except for categories of the businesses, which are represented by separate nodes labeled Category.</p>
</div>
<div class="paragraph">
<p>Graph model always depends on the application we have in mind for it.
Our application is to analyse ( inferred ) networks with graph algorithms.
If we were to use our graph as a recommendation engine, we might construct a different graph model.
Check this <a href="http://guides.neo4j.com/sandbox/recommendations">great guide</a> or this <a href="https://www.youtube.com/watch?v=oMTmG4ClO5I">educational video</a> on how you can use Neo4j as a recommendation engine.</p>
</div>
</div>
<div class="sect2">
<h3 id="_import"><a class="link" href="#_import">Import</a></h3>
<div class="listingblock">
<div class="title">Define graph schema (constraint/index)</div>
<div class="content">
<pre class="highlight"><code class="language-cypher" data-lang="cypher">CALL apoc.schema.assert(
{Category:['name']},
{Business:['id'],User:['id'],Review:['id']});</code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">Load businesses</div>
<div class="content">
<pre class="highlight"><code class="language-cypher" data-lang="cypher">CALL apoc.periodic.iterate("
CALL apoc.load.json('file:///dataset/business.json') YIELD value RETURN value
","
MERGE (b:Business{id:value.business_id})
SET b += apoc.map.clean(value, ['attributes','hours','business_id','categories','address','postal_code'],[])
WITH b,value.categories as categories
UNWIND categories as category
MERGE (c:Category{id:category})
MERGE (b)-[:IN_CATEGORY]->(c)
",{batchSize: 10000, iterateList: true});</code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">Load tips</div>
<div class="content">
<pre class="highlight"><code class="language-cypher" data-lang="cypher">CALL apoc.periodic.iterate("
CALL apoc.load.json('file:///dataset/tip.json') YIELD value RETURN value
","
MATCH (b:Business{id:value.business_id})
MERGE (u:User{id:value.user_id})
MERGE (u)-[:TIP{date:value.date,likes:value.likes}]->(b)
",{batchSize: 20000, iterateList: true});</code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">Load reviews</div>
<div class="content">
<pre class="highlight"><code class="language-cypher" data-lang="cypher">CALL apoc.periodic.iterate("
CALL apoc.load.json('file:///dataset/review.json')
YIELD value RETURN value
","
MERGE (b:Business{id:value.business_id})
MERGE (u:User{id:value.user_id})
MERGE (r:Review{id:value.review_id})
MERGE (u)-[:WROTE]->(r)
MERGE (r)-[:REVIEWS]->(b)
SET r += apoc.map.clean(value, ['business_id','user_id','review_id','text'],[0])
",{batchSize: 10000, iterateList: true});</code></pre>
</div>
</div>
<div class="listingblock">
<div class="title">Load users</div>
<div class="content">
<pre class="highlight"><code class="language-cypher" data-lang="cypher">CALL apoc.periodic.iterate("
CALL apoc.load.json('file:///dataset/user.json')
YIELD value RETURN value
","
MERGE (u:User{id:value.user_id})
SET u += apoc.map.clean(value, ['friends','user_id'],[0])
WITH u,value.friends as friends
UNWIND friends as friend
MERGE (u1:User{id:friend})
MERGE (u)-[:FRIEND]-(u1)
",{batchSize: 100, iterateList: true});</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_networks"><a class="link" href="#_networks">Networks</a></h3>
<div class="sect3">
<h4 id="_social_network"><a class="link" href="#_social_network">Social network</a></h4>
<div class="paragraph">
<p><a href="https://en.wikipedia.org/wiki/Social_network">Social network</a> is a theoretical construct useful in the social sciences to study relationships between individuals, groups, organizations, or even entire societies.
An axiom of the social network approach to understanding social interaction is that social phenomena should be primarily conceived and investigated through the properties of relationships between and within nodes, instead of the properties of these nodes themselves.
Precisely because many different types of relations, singular or in combination, form these network configurations, network analytics are useful to a broad range of research enterprises.</p>
</div>
<div class="paragraph">
<p><a href="https://en.wikipedia.org/wiki/Social_network_analysis">Social network analysis</a> is the process of investigating social structures through the use of networks and graph theory.
It characterizes networked structures in terms of nodes (individual actors, people, or things within the network) and the ties, edges, or links (relationships or interactions) that connect them.
Examples of social structures commonly visualized through social network analysis include social media networks, memes spread, friendship and acquaintance networks, collaboration graphs, kinship, disease transmission.</p>
</div>
<div class="paragraph">
<p>Social network analysis has emerged as a key technique in modern sociology.
It has also gained a significant following in anthropology, biology, demography, communication studies, economics, geography, history, information science, organizational studies, political science, social psychology, development studies, sociolinguistics, and computer science.</p>
</div>
<div class="paragraph">
<p>Yelp’s friendship network is an <em>undirected</em> graph with <em>unweighted</em> friend relationships between users.
There are 507948 users with no friends. They will be ignored in our analysis.</p>
</div>
<div class="sect4">
<h5 id="_global_graph_statistics"><a class="link" href="#_global_graph_statistics">Global graph statistics:</a></h5>
<div class="paragraph">
<p>Nodes : 8981389</p>
</div>
<div class="paragraph">
<p>Relationships : 35444850</p>
</div>
<div class="paragraph">
<p>Weakly connected components : 18512</p>
</div>
<div class="paragraph">
<p>Nodes in largest WCC : 8938630</p>
</div>
<div class="paragraph">
<p>Edges in largest WCC : 35420520</p>
</div>
<div class="paragraph">
<p>Triangle count :</p>
</div>
<div class="paragraph">
<p>Average clustering coefficient :</p>
</div>
<div class="paragraph">
<p>Graph diameter (longest shortest path):</p>
</div>
</div>
<div class="sect4">
<h5 id="_local_graph_statistics"><a class="link" href="#_local_graph_statistics">Local graph statistics:</a></h5>
<div class="listingblock">
<div class="title">Use apoc to calculate local statistics</div>
<div class="content">
<pre class="highlight"><code class="language-cypher" data-lang="cypher">MATCH (u:User)
RETURN avg(apoc.node.degree(u,'FRIEND')) as average_friends,
stdev(apoc.node.degree(u,'FRIEND')) as stdev_friends,
max(apoc.node.degree(u,'FRIEND')) as max_friends,
min(apoc.node.degree(u,'FRIEND')) as min_friends</code></pre>
</div>
</div>
<div class="paragraph">
<p>Average number of friends : 7.47</p>
</div>
<div class="paragraph">
<p>Standard deviation of friends : 46.96</p>
</div>
<div class="paragraph">
<p>Minimum count of friends : 1</p>
</div>
<div class="paragraph">
<p>Maximum count of friends : 14995</p>
</div>
<div class="paragraph">
<p>Prior work:</p>
</div>
<div class="ulist">
<ul>
<li>
<p><a href="http://snap.stanford.edu/class/cs224w-2015/projects_2015/Predicting_Yelp_Ratings_From_Social_Network_Data.pdf" class="bare">http://snap.stanford.edu/class/cs224w-2015/projects_2015/Predicting_Yelp_Ratings_From_Social_Network_Data.pdf</a></p>
</li>
<li>
<p><a href="https://arxiv.org/pdf/1512.06915.pdf" class="bare">https://arxiv.org/pdf/1512.06915.pdf</a></p>
</li>
<li>
<p><a href="http://trust.sce.ntu.edu.sg/wit-ec16/paper/davoust.pdf" class="bare">http://trust.sce.ntu.edu.sg/wit-ec16/paper/davoust.pdf</a></p>
</li>
</ul>
</div>
</div>
</div>
<div class="sect3">
<h4 id="_projecting_a_review_co_occurence_graph"><a class="link" href="#_projecting_a_review_co_occurence_graph">Projecting a review co-occurence graph</a></h4>
<div class="paragraph">
<p>We can try to find which businesses are often reviewed by same users by inferring a <a href="https://en.wikipedia.org/wiki/Co-occurrence_networks">co-occurence network</a> between them.
By way of definition, co-occurrence networks are the collective interconnection of nodes based on their paired presence within a specified domain.
Our network is generated by connecting pairs of businesses using a set of criteria defining co-occurrence.</p>
</div>
<div class="paragraph">
<p>The co-occurence criteria for this network is that any pair of businesses must have at least 5 common reviewers.
We save the count of common reviewers as a property of the relationship that will be used as a weight in community detection analysis.
Inferred graph is <em>undirected</em>, as changing the direction of the relationships does not imply any semantic difference.
We will limit our network to those businesses, that have more than 10 reviews and project a co-occurent relationship between businesses.</p>
</div>
<div class="listingblock">
<div class="title">Project a review co-occurence between businesses</div>
<div class="content">
<pre class="highlight"><code class="language-cypher" data-lang="cypher">CALL apoc.periodic.iterate('
MATCH (b1:Business)
WHERE size((b1)<-[:REVIEWS]->()) > 10 AND b1.city="Las Vegas"
RETURN b1
','
MATCH (b1)<-[:REVIEWS]-(r1)
MATCH (r1)<-[:WROTE]-(u)
MATCH (u)-[:WROTE]->(r2)
MATCH (r2)-[:REVIEWS]->(b2)
WHERE id(b1) < id(b2) AND b2.city="Las Vegas"
WITH b1, b2, COUNT(*) AS weight where weight > 5
MERGE (b1)-[cr:CO_OCCURENT_REVIEWS]-(b2)
ON CREATE SET cr.weight = weight
',{batchSize: 1});</code></pre>
</div>
</div>
<div class="paragraph">
<p>Prior work:</p>
</div>
</div>
<div class="sect3">
<h4 id="_projecting_a_review_similarity_graph"><a class="link" href="#_projecting_a_review_similarity_graph">Projecting a review similarity graph</a></h4>
<div class="paragraph">
<p>We can try to find similar groups of users by projecting a review similiarity network between them.
The idea is to start with users that have more than 10 reviews and find all pairs of users who have reviewed more than 10 common businesses.
We do this to filter out users with not enough data.
We could do something similar to filter out users who have reviewed every business (probably bot or bored).
Once we find pairs of users we calculate their similarity of reviews using cosine similarity and only create a relationship if cosine similarity is greater than 0, sometimes also called hard similarity.
We do this so we do not end up with complete graph, where every pair of users is connected.
Most community detection algorithms perform poorly in a complete graph.
Cosine similarity between pairs of users is saved as a property of relationship and can be used as a weight in graph algorithms.
Projected graph is modeled <em>undirected</em> as the direction of the relationship have no semantic value.</p>
</div>
<div class="paragraph">
<p>Projecting a review similarity graph is often used in recommendations. We calculate who are similar users based on review ratings, so we can recommend to a user what similar users liked.</p>
</div>
<div class="listingblock">
<div class="title">Create a review similarity graph</div>
<div class="content">
<pre class="highlight"><code class="language-cypher" data-lang="cypher">CALL apoc.periodic.iterate(
"MATCH (p1:User) WHERE size((p1)-[:WROTE]->()) > 5 RETURN p1",
"
MATCH (p1)-[:WROTE]->(r1)-->()<--(r2)<-[:WROTE]-(p2)
WHERE id(p1) < id(p2) AND size((p2)-[:WROTE]->()) > 10
WITH p1,p2,count(*) as coop, collect(r1.stars) as s1, collect(r2.stars) as s2 where coop > 10
WITH p1,p2, apoc.algo.cosineSimilarity(s1,s2) as cosineSimilarity WHERE cosineSimilarity > 0
MERGE (p1)-[s:SIMILAR_REVIEWS]-(p2) SET s.weight = cosineSimilarity"
, {batchSize:100, parallel:false,iterateList:true});</code></pre>
</div>
</div>
<div class="paragraph">
<p>Prior work:</p>
</div>
<div class="ulist">
<ul>
<li>
<p><a href="http://snap.stanford.edu/class/cs224w-2015/projects_2015/Predicting_Yelp_Ratings_Using_User_Friendship_Network_Information.pdf" class="bare">http://snap.stanford.edu/class/cs224w-2015/projects_2015/Predicting_Yelp_Ratings_Using_User_Friendship_Network_Information.pdf</a></p>
</li>
<li>
<p><a href="http://snap.stanford.edu/class/cs224w-2013/projects2013/cs224w-038-final.pdf" class="bare">http://snap.stanford.edu/class/cs224w-2013/projects2013/cs224w-038-final.pdf</a></p>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_overview_of_algorithm_procedures"><a class="link" href="#_overview_of_algorithm_procedures">Overview of Algorithm Procedures</a></h2>
<div class="sectionbody">
<table id="table-all" class="tableblock frame-all grid-all spread">
</table>
</div>
</div>
<div class="sect1">
<h2 id="_algorithms_2"><a class="link" href="#_algorithms_2">Algorithms</a></h2>
<div class="sectionbody">
<div class="paragraph">
<p>Graph algorithms are used to compute metrics for graphs, nodes or relationships.</p>
</div>
<div class="paragraph">
<p>They can provide insights on relevant entities (centralities, ranking) in the graph or inherent structures like communities (community-detection, graph-partitioning, clustering).</p>
</div>
<div class="paragraph">
<p>Many of them are iterative aproaches that frequently traverse the graph for the computation using random walks, breadth-first- or depth-first searches or pattern matching.</p>
</div>
<div class="paragraph">
<p>Due to the exponential growth of possible paths with increasing distance many of the approaches are also of a high algorithmic complexity.</p>
</div>
<div class="paragraph">
<p>Fortunately some optimized algorithms exist that utilize certain structures of the graph, memoize of already explored parts and if possible parallelize operations.
Whenever possible we tried to apply these optimizations.</p>
</div>
<div class="sect2">
<h3 id="_community_detection_triangle_counting_clustering_coefficient"><a class="link" href="#_community_detection_triangle_counting_clustering_coefficient">Community detection: Triangle Counting / Clustering Coefficient</a></h3>
<div class="paragraph">
<p>Triangle counting is a community detection graph algorithm which is used to determine the number of triangles passing through each node in the graph. A node is part of a triangle when it has two linked nodes with an relationship between.
The triangle is a three-node subgraph, where every two nodes are connected.[1]</p>
</div>
<div class="sect3">
<h4 id="_history_explanation"><a class="link" href="#_history_explanation">History, Explanation</a></h4>
<div class="paragraph">
<p>Counting the number of triangles in a graph is a fundamental problem with various applications.
The problem has been studied before from a theoretic point of view.
It can be seen as a special case of counting given length cycles.
On the other hand, counting triangles is a basic issue in network analysis.
Due to the increasing interest in analyzing large networks like the Internet, the WWW or social networks, the computation of network indices based on counting triangles has become an often used tool in network analysis.
For example, the so-called clustering coefficient is frequently quoted as an important index for measuring the concentration of clusters in graphs respectively its tendency to decompose into communities.
The local clustering coefficient of a node v is defined as the likeliness that two neighbors u and w of v are also connected, while the clustering coefficient of a graph is just the normalized sum of the clustering coefficient of its nodes.
Accordingly, its computation involves counting the number of triangles.
Similarly the transitivity coefficient of a graph, which is just three times the number of triangles divided by the number of triples (paths of length two) in the graph is sometimes considered.[2]</p>
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<h4 id="_when_to_use_it_use_cases"><a class="link" href="#_when_to_use_it_use_cases">When to use it / use-cases</a></h4>