# Algorithm overview¶

Graph computing can detect the graph structure, such as the communities in a graph and the division of a graph. It can also reveal the inherent characteristics of the correlation between various vertexes, such as the centrality and similarity of the vertices. This topic introduces the algorithms and parameters supported by Nebula Graph.

Note

This topic only introduces the parameters of Nebula Analytics. For details about the parameters of Nebula Algorithm, see algorithm.

Note

The algorithm parameters need to be set when performing graph computing, and there are requirements for data sources. The data source needs to contain source vertexes and destination vertexes. PageRank, DegreeWithTime, SSSP, APSP, LPA, HANP, and Louvain algorithms must include weight.

• If the data source comes from HDFS, users need to specify a CSV file that contains src and dst columns. Some algorithms also need to contain a weight column.
• If the data source comes from Nebula Graph, users need to specify the edge types that provide src and dst columns. Some algorithms also need to specify the properties of the edge types as weight columns.

## Node importance measurement¶

### PageRank¶

The PageRank algorithm calculates the relevance and importance of vertices based on their relationships. It is commonly used in search engine page rankings. If a page is linked by many other pages, the page is more important (PageRank value is higher). If a page with a high PageRank value links to other pages, the PageRank value of the linked pages will increase.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
ITERATIONS 10 The maximum number of iterations.
IS_DIRECTED true Whether to consider the direction of the edges. If set to false, the system automatically adds the reverse edge.
EPS 0.0001 The convergence accuracy. When the difference between the result of two iterations is less than the EPS value, the iteration is not continued.
DAMPING 0.85 The damping coefficient. It is the jump probability after visiting a page.
• Output parameters

Parameter Type Description
VID Determined by vid_type The vertex ID.
VALUE double The PageRank value of the vertex.

### KCore¶

The KCore algorithm is used to calculate the subgraph composed of no vertexes less than K degree, usually used in community discovery, financial risk control and other scenarios. The calculation result is one of the most commonly used reference values to judge the importance of a vertex, which reflects the propagation ability of a vertex.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
TYPE vertex The calculation type. Available values are vertex and subgraph. When set to vertex, the system calculates the number of cores for each vertex.
KMIN 1 Set the minimum value of K when performing the range calculation. Takes effect only when TYPE=subgraph.
KMAX 1000000 Set the maximum value of K when performing the range calculation. Takes effect only when TYPE=subgraph.
• Output parameters when TYPE=vertex

Parameter Type Description
VID Determined by vid_type The vertex ID.
VALUE int Outputs the core degree of the vertex.
• Output parameters when TYPE=subgraph

Parameter Type Description
VID Determined by vid_type The vertex ID.
VALUE The same with VID Outputs the neighbors of the vertex.

### DegreeCentrality (NStepDegree)¶

The DegreeCentrality algorithm is used to find the popular vertexes in a graph. Degree centrality measures the number of incoming or outgoing (or both) relationships from a vertex, depending on the direction of the projection of the relationship. The greater the degree of a vertex is, the higher the degree centrality of the vertex is, and the more important the vertex is in the network.

Note

Nebula Analytics only estimates DegreeCentrality roughly.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
IS_DIRECTED true Whether to consider the direction of the edges. If set to false, the system automatically adds the reverse edge.
STEP 3 The degree of calculation. -1 means infinity.
BITS 6 The hyperloglog bit width for cardinality estimation.
TYPE both The direction of the edges for calculation. Optional values are in, out and both.
• Output parameters when TYPE=both

Parameter Type Description
VID Determined by vid_type The vertex ID.
BOTH_DEGREE int Outputs the bidirectional degree centrality of the vertex.
OUT_DEGREE int Outputs the outbound degree centrality of the vertex.
IN_DEGREE int Outputs the inbound degree centrality of the vertex.
• Output parameters when TYPE=out

Parameter Type Description
VID Determined by vid_type The vertex ID.
OUT_DEGREE int Outputs the outbound degree centrality of the vertex.
• Output parameters when TYPE=in

Parameter Type Description
VID Determined by vid_type The vertex ID.
IN_DEGREE int Outputs the inbound degree centrality of the vertex.

### DegreeWithTime¶

The DegreeWithTime algorithm is used to count neighbors based on the time range of edges to find out the popular vertexes in a graph.

Note

This algorithm is supported by Nebula Analytics only.

Parameter descriptions are as follows:

• Input parameters

Parameter Predefined value Description
ITERATIONS 10 The maximum number of iterations.
IS_DIRECTED true Whether to consider the direction of the edges. If set to false, the system automatically adds the reverse edge.
BEGIN_TIME - The begin time.
END_TIME - The end time.
• Output parameters when TYPE=both

Parameter Type Description
VID Determined by vid_type The vertex ID.
BOTH_DEGREE int Outputs the bidirectional popularity of the vertex.
OUT_DEGREE int Outputs the outbound popularity of the vertex.
IN_DEGREE int Outputs the inbound popularity of the vertex.
• Output parameters when TYPE=out

Parameter Type Description
VID Determined by vid_type The vertex ID.
OUT_DEGREE int Outputs the outbound popularity of the vertex.
• Output parameters when TYPE=in

Parameter Type Description
VID Determined by vid_type The vertex ID.
IN_DEGREE int Outputs the inbound popularity of the vertex.

### BetweennessCentrality¶

The BetweennessCentrality algorithm is used to detect the amount of influence a vertex has on the flow of information in a graph. It is used to find the vertexes that act as bridges between one part of the graph and another. Each vertex is given a score, the betweenness centrality score, based on the number of shortest paths through that vertex.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
ITERATIONS 10 The maximum number of iterations.
IS_DIRECTED true Whether to consider the direction of the edges. If set to false, the system automatically adds the reverse edge.
CHOSEN -1 The selected vertex ID, -1 means random selection.
CONSTANT 2 The constant.
• Output parameters

Parameter Type Description
VID Determined by vid_type The vertex ID.
VALUE double The betweenness centrality score of the vertex.

### ClosenessCentrality¶

The ClosenessCentrality algorithm is used to calculate the reciprocal of the average of the shortest distance from one vertex to all other reachable vertexes. The larger the value is, the closer the vertex is to the center of the graph, and it can also be used to measure how long it takes for information to be transmitted from that vertex to other vertexes.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
IS_DIRECTED true Whether to consider the direction of the edges. If set to false, the system automatically adds the reverse edge.
NUM_SAMPLES 10 The number of sample vertices.
• Output parameters

Parameter Type Description
VID Determined by vid_type The vertex ID.
VALUE double The closeness centrality score of the vertex.

## Path¶

### APSP¶

The APSP (Full Graph Shortest Path) algorithm is used to find all shortest paths between two vertexes in a graph.

Note

This algorithm is supported by Nebula Analytics only.

Parameter descriptions are as follows:

• Output parameters

Parameter Type Description
VID1 Determined by vid_type The VID of the source vertex.
VID2 Determined by vid_type The VID of the destination vertex.
DISTANCE double Outputs the distance from VID1 to VID2.

### SSSP¶

The SSSP (Single source shortest Path) algorithm is used to calculate the shortest path length from a given vertex (source vertex) to other vertexes. It is usually used in scenarios such as network routing and path designing.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
ROOT - The VID of the source vertex.
• Output parameters

Parameter Type Description
VID Determined by vid_type The VID of the source vertex.
DISTANCE double Outputs the distance from ROOT to VID.

### BFS¶

The BFS (Breadth First traversal) algorithm is a basic graph traversal algorithm. It gives a source vertex and accesses other vertexes with increasing hops, that is, it traverses all the adjacent vertexes of the vertex first and then extends to the adjacent vertexes of the adjacent vertexes.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
IS_DIRECTED true Whether to consider the direction of the edges. If set to false, the system automatically adds the reverse edge.
ROOT - The VID of the source vertex.
• Output parameters

Parameter Type Description
ROOT Determined by vid_type The VID of the source vertex.
VISITED int Outputs the number of the vertex accessed by ROOT.

## Community discovery¶

### LPA¶

The LPA (label propagation) algorithm is a semi-supervised learning method based on graph. Its basic idea is to use label information of labeled vertexes to predict label information of unlabeled vertexes. vertexes include labeled and unlabeled data, and their edges represent the similarity of two vertexes. The labels of vertexes are transferred to other vertexes according to the similarity. Label data is like a source that can be labeled for unlabeled data. The greater the similarity of vertexes is, the easier the label is to spread.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
ITERATIONS 10 The maximum number of iterations.
IS_DIRECTED true Whether to consider the direction of the edges. If set to false, the system automatically adds the reverse edge.
IS_CALC_MODULARITY false Whether to calculate modularity.
• Output parameters

Parameter Type Description
VID Determined by vid_type The vertex ID.
LABEL The same with VID Outputs the vertex IDs that have the same label.

### HANP¶

The HANP (Hop Preference & Node Preference) algorithm is an optimization algorithm of LPA algorithm, which considers other information of labels, such as degree information, distance information, etc., and introduces attenuation coefficient during propagation to prevent transition propagation.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
ITERATIONS 10 The maximum number of iterations.
IS_DIRECTED true Whether to consider the direction of the edges. If set to false, the system automatically adds the reverse edge.
PREFERENCE 1.0 The bias of the neighbor vertex degree. m>0indicates biasing the neighbor with high vertex degree, m<0 indicates biasing the neighbor with low vertex degree, and m=0 indicates ignoring the neighbor vertex degree.
HOP_ATT 0.1 The attenuation coefficient. The value ranges from 0 to 1. The larger the value, the faster it decays and the fewer times it can be passed.
• Output parameters

Parameter Type Description
VID Determined by vid_type The vertex ID.
LABEL The same with VID Outputs the vertex IDs that have the same label.

### ConnectedComponent¶

The ConnectedComponent algorithm is used to calculate a subgraph of a graph in which all vertexes are connected to each other. Strongly Connected Component takes the path direction into account, while Weakly Connected Component does not.

Note

Nebula Analytics only supports Weakly Connected Component.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
IS_DIRECTED true Whether to consider the direction of the edges. If set to false, the system automatically adds the reverse edge.
IS_CALC_MODULARITY false Whether to calculate modularity.
• Output parameters

Parameter Type Description
VID Determined by vid_type The vertex ID.
LABEL The same with VID Outputs the vertex IDs that have the same label.

### Louvain¶

The Louvain algorithm is a community discovery algorithm based on modularity. This algorithm performs well in efficiency and effect, and can be used to find hierarchical community structures. Its optimization goal is to maximize the modularity of the whole community network. Modularity is used to distinguish the differences in link density within and between communities, and to measure how well each vertex divides the community. In general, a good clustering approach will result in more modularity within communities than between communities.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
IS_DIRECTED true Whether to consider the direction of the edges. If set to false, the system automatically adds the reverse edge.
OUTER_ITERATION 20 The maximum number of iterations in the first phase.
INNER_ITERATION 10 The maximum number of iterations in the second phase.
IS_CALC_MODULARITY false Whether to calculate modularity.
• Output parameters

Parameter Type Description
VID Determined by vid_type The vertex ID.
LABEL The same with VID Outputs the vertex IDs that have the same label.

## Graph feature¶

### TriangleCount¶

The TriangleCount algorithm is used to count the number of triangles in a graph. The more triangles, the higher the degree of vertex association in the graph, the tighter the organizational relationship.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
OPT 3 The calculation type. Optional values are 1, 2 and 3. 1 indicates counting the entire graph, 2 indicates counting through each vertex, 3 indicates listing all triangles.
REMOVED_DUPLICATION_EDGE true Whether to exclude repeated edges.
REMOVED_SELF_EDGE true Whether to exclude self-loop edge.
• Output parameters when OPT=1

Parameter Type Description
COUNT int Outputs the number of the triangles in the full graph space.
• Output parameters when OPT=2

Parameter Type Description
VID Determined by vid_type The vertex ID.
COUNT int Outputs the number of the triangles based on the vertex.
• Output parameters when OPT=3

Parameter Type Description
VID1 The same with VID Outputs the ID of the vertex A that forms the triangle.
VID2 The same with VID Outputs the ID of the vertex B that forms the triangle.
VID3 The same with VID Outputs the ID of the vertex C that forms the triangle.

## Clustering¶

### ClusteringCoefficient¶

The ClusteringCoefficient algorithm is used to calculate the clustering degree of vertexes in a graph. In all kinds of network structures reflecting the real world, especially social network structures, network groups with relatively high density tend to be formed between various vertexes. In other words, compared with the networks randomly connected between two vertexes, the aggregation coefficient of the real world network is higher.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
TYPE local The clustering type. Optional values are local and global. local indicates counting through each vertex, global indicates counting the entire graph.
REMOVED_DUPLICATION_EDGE true Whether to exclude repeated edges.
REMOVED_SELF_EDGE true Whether to exclude self-loop edge.
• Output parameters when TYPE=local

Parameter Type Description
VID Determined by vid_type The vertex ID.
VALUE double Outputs the clustering coefficient of the vertex.
• Output parameters when TYPE=global

Parameter Type Description
VID Determined by vid_type The vertex ID.
VALUE double Outputs the clustering coefficient of the full graph space. There is only one line of data.

## Similarity¶

### Jaccard¶

The Jaccard algorithm is used to calculate the similarity of two vertexes (or sets) and predict the relationship between them. It is suitable for social network friend recommendation, relationship prediction and other scenarios.

Parameter descriptions are as follows:

• Nebula Analytics

• Input parameters

Parameter Predefined value Description
IDS1 - A set of VIDs. Multiple VIDs are separated by commas (,). It is not allowed to be empty.
IDS2 - A set of VIDs. Multiple VIDs are separated by commas (,). It can be empty, and empty represents all vertexes.
REMOVED_SELF_EDGE true Whether to exclude self-loop edges.
• Output parameters

Parameter Type Description
VID1 Determined by vid_type The ID of the first vertex.
VID2 Determined by vid_type The ID of the second vertex.
VALUE double The similarity between VID1 and VID2.

Last update: August 12, 2022