I have a graph database in which there is a root vertex with some "id= Xyz".This vertex is related to 3 more vertices with an edge having relationship of a "child".
Now these 3 vertices themselves have 2 connected vertices each with the same relationship as "child".
I want to get the info of all the directly or indirectly connected vertices keeping the nested structure maintained.
The JSON output should be in the nested form for indirect vertices.
Can we do this ?
And what to do if the depth of tree increase to n
Please help
Not sure how you want your data to look like, but you can do this in several ways:
Using path for a full tree:
g.V().hasLabel('root').emit().repeat(out()).path()
If you want only the two levels:
g.V().hasLabel('root').emit().repeat(out()).times(2).path()
You can also use project step if you want specific data structure:
g.V().hasLabel('root').project('v', 'c').
by(id).
by(out().project('v', 'c').by(id).
by(out().id().fold()).fold())
example: https://gremlify.com/at
I'm working in C, using the igraph library. I need to get the minimum spanning tree of a given graph stores in a igraph_graph_t type (g). Also I have a igraph_vector containing the weight of each edge (w). The following is my call:
igraph_minimum_spanning_tree_prim(&g, &mst, &w)
How I can get the weight of each edge in the mst graph? All I need is the cost of mst.
Thanks, Guillermo.
I think you should take the result graph(mst) and sum the weight of the edges.
I have a large, non-cyclic directed graph.
Every node has some key/value pairs. Some of the keys can be searched by range.
Let's say all nodes have these keys:
color - red, blue, green, etc.
price - an integer
size - an integer
I want to select a list of nodes from my graph such that:
all nodes have color = red
all nodes have price >= 10 and <= 20
the list is ordered by increasing size
any node that meets the criteria for color and price and has no outlinks (no edges go from that node) is in the list
no two nodes in the list share an edge
Ideally, the list would have the maximum number of nodes possibly to satisfy all those constraints.
I need to be able to search this graph very quickly.
What kind of data store (graph or otherwise) is best suited for this problem? Any hints on how to implement schema and query to get the best performance?
Do you have any size estimations on this? That would give some more hints on how you can do the computations - in memory or index or lazy graph loading. /peter neubauer
I'm willing to store a Property Graph into HBase. A Property Graph is a graph nodes and edges have properties and multiple edges can link the same tuple of nodes as long as the edges belong to different types.
My query pattern will be either asking for properties and neighborhood or traversing the graph. An example is: Vertex[name=claudio]=>OutgoingEdge[knows]=>Vertex[gender=female], which will give me all the female people that claudio likes.
I know that a graph database does just this, but they usually don't scale on multiple nodes in case of a huge dataset. So I'm willing to implement this on a NoSQL ColumnStore (HBase, Cassandra...)
My datamodel follows.
Vertices Table:
key: vertexid (uuid)
Family "Properties:": <property name>=><property value>, ...
Family "OutgoingEdges:": <edge key>=><other vertexid>, ...
Family "IncomingEdges:": same as outgoing edges...
This table allows me to fetch quickly the properties of a vertex and
its adjacency list. I can't use the vertexid as the other endpoint
because multiple edges (with different types) can connect the same two
vertices.
Edges Table:
key: edge key (composite(<source vertexid>, <destination vertexid>,
<edge typename>)) (i.e. vertexid1_vertexid2_knows)
Family "Properties:": <property name>=><property value>, ...
This table allows me to fetch quickly the properties of an edge.
Edges Types:
key: composite(<source vertexid>, "out|in", <edge typename>) (i.e.
vertexid1_out_knows)
Family "Neighbor:": <destination vertexid>=>null,...
This table allows me to search/scan for edges that are either incoming
or outgoing from a vertex and belong to specific type and would be the
core of the traversing ability of the API (so i want it to be as fast as
possible both in terms of network I/O (RPCs), disk I/O (seek)). It
should also "scale" on the size of the graph, meaning that with the
growth of the graph the cost of this type of operation should depend on
the number of edges outgoing from the vertex and not on the total number
of vertices and edges.
The example above i'd be considering vertexid1 the source vertex with
property name:claudio i'd scan vertexid1_out_knows and receive the list of
vertices connected. After that i can scan on the column
"Properties:gender" on these vertices and look for those having the
"female" value.
Questions:
1) General: do you see a better data model for my operations?
2) Can i fit everything in one table where for certain keys some
families would be empty (i.e. the "OutgoingEdges:" family would not make
sense for the edges)? I'd like that because as you can see all the keys
are composed by the vertexid uuid prefix, so they would be very compact
and fit mostly on the same regionserver.
3) I guess that for the scanning I'd make extensive use of Filters. I
guess regexp Filter will be my friend. Do you have concerns about
performance of filters applied to this data model?
This type of model looks like a sensible starting point for Cassandra (don't know much about HBase) - but for any distributed store you will run up against problems when traversing, because traversals will cross multiple nodes.
This is why dedicated graph databases such as Neo4J use a single-node design, and try to keep all data in RAM.
Looking up properties of particular nodes or edges should work well and scale horizontally - Twitter's FlockDB (now apparently abandoned) was a notable example of this.
You also need to consider whether you need lookups other than by ID (i.e. do you need any indexes)?
The deadline for this project is closing in very quickly and I don't have much time to deal with what it's left. So, instead of looking for the best (and probably more complicated/time consuming) algorithms, I'm looking for the easiest algorithms to implement a few operations on a Graph structure.
The operations I'll need to do is as follows:
List all users in the graph network given a distance X
List all users in the graph network given a distance X and the type of relation
Calculate the shortest path between 2 users on the graph network given a type of relation
Calculate the maximum distance between 2 users on the graph network
Calculate the most distant connected users on the graph network
A few notes about my Graph implementation:
The edge node has 2 properties, one is of type char and another int. They represent the type of relation and weight, respectively.
The Graph is implemented with linked lists, for both the vertices and edges. I mean, each vertex points to the next one and each vertex also points to the head of a different linked list, the edges for that specific vertex.
What I know about what I need to do:
I don't know if this is the easiest as I said above, but for the shortest path between 2 users, I believe the Dijkstra algorithm is what people seem to recommend pretty often so I think I'm going with that.
I've been searching and searching and I'm finding it hard to implement this algorithm, does anyone know of any tutorial or something easy to understand so I can implement this algorithm myself? If possible, with C source code examples, it would help a lot. I see many examples with math notations but that just confuses me even more.
Do you think it would help if I "converted" the graph to an adjacency matrix to represent the links weight and relation type? Would it be easier to perform the algorithm on that instead of the linked lists? I could easily implement a function to do that conversion when needed. I'm saying this because I got the feeling it would be easier after reading a couple of pages about the subject, but I could be wrong.
I don't have any ideas about the other 4 operations, suggestions?
List all users in the graph network given a distance X
A distance X from what? from a starting node or a distance X between themselves? Can you give an example? This may or may not be as simple as doing a BF search or running Dijkstra.
Assuming you start at a certain node and want to list all nodes that have distances X to the starting node, just run BFS from the starting node. When you are about to insert a new node in the queue, check if the distance from the starting node to the node you want to insert the new node from + the weight of the edge from the node you want to insert the new node from to the new node is <= X. If it's strictly lower, insert the new node and if it is equal just print the new node (and only insert it if you can also have 0 as an edge weight).
List all users in the graph network given a distance X and the type of relation
See above. Just factor in the type of relation into the BFS: if the type of the parent is different than that of the node you are trying to insert into the queue, don't insert it.
Calculate the shortest path between 2 users on the graph network given a type of relation
The algorithm depends on a number of factors:
How often will you need to calculate this?
How many nodes do you have?
Since you want easy, the easiest are Roy-Floyd and Dijkstra's.
Using Roy-Floyd is cubic in the number of nodes, so inefficient. Only use this if you can afford to run it once and then answer each query in O(1). Use this if you can afford to keep an adjacency matrix in memory.
Dijkstra's is quadratic in the number of nodes if you want to keep it simple, but you'll have to run it each time you want to calculate the distance between two nodes. If you want to use Dijkstra's, use an adjacency list.
Here are C implementations: Roy-Floyd and Dijkstra_1, Dijkstra_2. You can find a lot on google with "<algorithm name> c implementation".
Edit: Roy-Floyd is out of the question for 18 000 nodes, as is an adjacency matrix. It would take way too much time to build and way too much memory. Your best bet is to either use Dijkstra's algorithm for each query, but preferably implementing Dijkstra using a heap - in the links I provided, use a heap to find the minimum. If you run the classical Dijkstra on each query, that could also take a very long time.
Another option is to use the Bellman-Ford algorithm on each query, which will give you O(Nodes*Edges) runtime per query. However, this is a big overestimate IF you don't implement it as Wikipedia tells you to. Instead, use a queue similar to the one used in BFS. Whenever a node updates its distance from the source, insert that node back into the queue. This will be very fast in practice, and will also work for negative weights. I suggest you use either this or the Dijkstra with heap, since classical Dijkstra might take a long time on 18 000 nodes.
Calculate the maximum distance between 2 users on the graph network
The simplest way is to use backtracking: try all possibilities and keep the longest path found. This is NP-complete, so polynomial solutions don't exist.
This is really bad if you have 18 000 nodes, I don't know any algorithm (simple or otherwise) that will work reasonably fast for so many nodes. Consider approximating it using greedy algorithms. Or maybe your graph has certain properties that you could take advantage of. For example, is it a DAG (Directed Acyclic Graph)?
Calculate the most distant connected users on the graph network
Meaning you want to find the diameter of the graph. The simplest way to do this is to find the distances between each two nodes (all pairs shortest paths - either run Roy-Floyd or Dijkstra between each two nodes and pick the two with the maximum distance).
Again, this is very hard to do fast with your number of nodes and edges. I'm afraid you're out of luck on these last two questions, unless your graph has special properties that can be exploited.
Do you think it would help if I "converted" the graph to an adjacency matrix to represent the links weight and relation type? Would it be easier to perform the algorithm on that instead of the linked lists? I could easily implement a function to do that conversion when needed. I'm saying this because I got the feeling it would be easier after reading a couple of pages about the subject, but I could be wrong.
No, adjacency matrix and Roy-Floyd are a very bad idea unless your application targets supercomputers.
This assumes O(E log V) is an acceptable running time, if you're doing something online, this might not be, and it would require some higher powered machinery.
List all users in the graph network given a distance X
Djikstra's algorithm is good for this, for one time use. You can save the result for future use, with a linear scan through all the vertices (or better yet, sort and binary search).
List all users in the graph network given a distance X and the type of relation
Might be nearly the same as above -- just use some function where the weight would be infinity if it is not of the correct relation.
Calculate the shortest path between 2 users on the graph network given a type of relation
Same as above, essentially, just determine early if you match the two users. (Alternatively, you can "meet in the middle", and terminate early if you find someone on both shortest path spanning tree)
Calculate the maximum distance between 2 users on the graph network
Longest path is an NP-complete problem.
Calculate the most distant connected users on the graph network
This is the diameter of the graph, which you can read about on Math World.
As for the adjacency list vs adjacency matrix question, it depends on how densely populated your graph is. Also, if you want to cache results, then the matrix might be the way to go.
The simplest algorithm to compute shortest path between two nodes is Floyd-Warshall. It's just triple-nested for loops; that's it.
It computes ALL-pairs shortest path in O(N^3), so it may do more work than necessary, and will take a while if N is huge.