fix(analytical): make clustering support undirected graph

[acezen]

What do these changes do?

see #3711

Related issue number

Fixes #3711

[acezen]

hi, @doudoubobo, I have a question about the computational formula of clustering:

• in NetworkX the formula is
  [2 * T(v) / deg(v)*(deg(v) - 1)] in
  https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.cluster.clustering.html#networkx.algorithms.cluster.clustering
  but why our formula is [T(v) / deg(v)*(deg(v)-1]
  

  GraphScope/analytical_engine/apps/clustering/clustering.h

  Line 254 in 4a7e1ab

  ctx_data[v] = degree == 0 ? 0.0 : 1.0 * tricnt[v] / degree;

  ?

• what's the meaning and use of rec_degree in

  GraphScope/analytical_engine/apps/clustering/clustering.h

  Line 253 in 4a7e1ab

  global_degree[v] * (global_degree[v] - 1) - 2 * rec_degree[v];

[doudoubobo]

hi, @doudoubobo, I have a question about the computational formula of clustering:

• in NetworkX the formula is
  [2 * T(v) / deg(v)*(deg(v) - 1)] in
  https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.cluster.clustering.html#networkx.algorithms.cluster.clustering
  but why our formula is [T(v) / deg(v)*(deg(v)-1]
  

  GraphScope/analytical_engine/apps/clustering/clustering.h

  Line 254 in 4a7e1ab

  ctx_data[v] = degree == 0 ? 0.0 : 1.0 * tricnt[v] / degree;

  
  ?
• what's the meaning and use of rec_degree in

  GraphScope/analytical_engine/apps/clustering/clustering.h

  Line 253 in 4a7e1ab

  global_degree[v] * (global_degree[v] - 1) - 2 * rec_degree[v];

Q: why our formula is [T(v) / deg(v)*(deg(v)-1]?
A: In the implement method of triangle counting, I remember the real triangle counting number for undirected graph is 2.0 * T(v) and 1.0 * T(v) for directed graph (see https://en.wikipedia.org/wiki/Clustering_coefficient)

Q: what's the meaning and use of rec_degree?
A: See https://en.wikipedia.org/wiki/Clustering_coefficient, the k_i is defined as the neighbor number of a vertex. For a directed graph, if both src-->dst and dst-->src edges exist, the degree of src is 2 but the k_i is 1. rec_degree is used to handle such situation.

[acezen]

hi, @doudoubobo, since GraphScope only allow one MessageStrategy in one application:

GraphScope/analytical_engine/apps/clustering/clustering.h

Lines 47 to 48 in 988aa46

	static constexpr grape::MessageStrategy message_strategy =
	grape::MessageStrategy::kAlongEdgeToOuterVertex;

for undirected graph, the strategy should be kAlongOutgoingEdgeToOuterVertex and use SendMsgThroughOEdges to send message like triangle:

GraphScope/analytical_engine/apps/clustering/triangles.h

Lines 51 to 53 in 988aa46

	messages.SendMsgThroughOEdges<fragment_t, int>(frag, v,
	ctx.global_degree[v], tid);
	});

But for the reason above, I use SendMsgThroughEdges for both directed graph and undirected graph, and the test case is ok to pass.

GraphScope/analytical_engine/apps/clustering/clustering.h

Lines 62 to 63 in 988aa46

	messages.SendMsgThroughEdges<fragment_t, int>(
	frag, v, ctx.global_degree[v], tid);

Can you help me double check that SendMsgThroughEdges is ok for directed graph and undirected graph in the message passing between fragments? I don't want to bring another potential bug with the changes.

[doudoubobo]

hi, @doudoubobo, since GraphScope only allow one MessageStrategy in one application:

GraphScope/analytical_engine/apps/clustering/clustering.h

Lines 47 to 48 in 988aa46

	static constexpr grape::MessageStrategy message_strategy =
	grape::MessageStrategy::kAlongEdgeToOuterVertex;

for undirected graph, the strategy should be kAlongOutgoingEdgeToOuterVertex and use SendMsgThroughOEdges to send message like triangle:

GraphScope/analytical_engine/apps/clustering/triangles.h

Lines 51 to 53 in 988aa46

	messages.SendMsgThroughOEdges<fragment_t, int>(frag, v,
	ctx.global_degree[v], tid);
	});

But for the reason above, I use SendMsgThroughEdges for both directed graph and undirected graph, and the test case is ok to pass.

GraphScope/analytical_engine/apps/clustering/clustering.h

Lines 62 to 63 in 988aa46

	messages.SendMsgThroughEdges<fragment_t, int>(
	frag, v, ctx.global_degree[v], tid);

Can you help me double check that SendMsgThroughEdges is ok for directed graph and undirected graph in the message passing between fragments? I don't want to bring another potential bug with the changes.

For directed graph, since we set message_strategy = grape::MessageStrategy::kAlongEdgeToOuterVertex, SendMsgThroughOEdges and SendMsgThroughEdges should behave the same. Same for undirected graphs.

[acezen]

hi, @doudoubobo, since GraphScope only allow one MessageStrategy in one application:

GraphScope/analytical_engine/apps/clustering/clustering.h

Lines 47 to 48 in 988aa46

	static constexpr grape::MessageStrategy message_strategy =
	grape::MessageStrategy::kAlongEdgeToOuterVertex;

for undirected graph, the strategy should be kAlongOutgoingEdgeToOuterVertex and use SendMsgThroughOEdges to send message like triangle:

GraphScope/analytical_engine/apps/clustering/triangles.h

Lines 51 to 53 in 988aa46

	messages.SendMsgThroughOEdges<fragment_t, int>(frag, v,
	ctx.global_degree[v], tid);
	});

But for the reason above, I use SendMsgThroughEdges for both directed graph and undirected graph, and the test case is ok to pass.

GraphScope/analytical_engine/apps/clustering/clustering.h

Lines 62 to 63 in 988aa46

	messages.SendMsgThroughEdges<fragment_t, int>(
	frag, v, ctx.global_degree[v], tid);

Can you help me double check that SendMsgThroughEdges is ok for directed graph and undirected graph in the message passing between fragments? I don't want to bring another potential bug with the changes.

For directed graph, since we set message_strategy = grape::MessageStrategy::kAlongEdgeToOuterVertex, SendMsgThroughOEdges and SendMsgThroughEdges should behave the same. Same for undirected graphs.

thanks for the reply, since the approve dismiss by the fix push, can yo approve again to the PR.