@spec average_clustering_coefficient(Yog.graph()) :: float()

Calculates the average clustering coefficient for the entire graph.

Calculates the average density across all communities.

@spec clustering_coefficient(Yog.graph(), Yog.node_id()) :: float()

Calculates the local clustering coefficient for a node.

Measures how close the node's neighbors are to forming a complete clique. Range: [0.0, 1.0].

Examples

iex> graph = Yog.undirected()
...> |> Yog.add_node(1, nil) |> Yog.add_node(2, nil) |> Yog.add_node(3, nil)
...> |> Yog.add_edge_ensure(from: 1, to: 2, with: 1)
...> |> Yog.add_edge_ensure(from: 2, to: 3, with: 1)
...> |> Yog.add_edge_ensure(from: 3, to: 1, with: 1)
iex> Yog.Community.Metrics.clustering_coefficient(graph, 1)
1.0

@spec community_density(Yog.graph(), MapSet.t(Yog.node_id())) :: float()

Calculates the density of edges within a specific set of nodes.

@spec count_triangles(Yog.graph()) :: integer()

Counts the total number of triangles in the graph.

A triangle is a set of three nodes where each pair is connected. Uses neighbor intersection algorithm: O(Σ deg(v)²).

Examples

iex> graph = Yog.undirected()
...> |> Yog.add_node(1, nil) |> Yog.add_node(2, nil) |> Yog.add_node(3, nil)
...> |> Yog.add_edge_ensure(from: 1, to: 2, with: 1)
...> |> Yog.add_edge_ensure(from: 2, to: 3, with: 1)
...> |> Yog.add_edge_ensure(from: 3, to: 1, with: 1)
iex> Yog.Community.Metrics.count_triangles(graph)
1

@spec density(Yog.graph()) :: float()

Calculates the graph density.

@spec modularity(Yog.Graph.t(), any(), any()) :: any()

Calculates modularity for a given community partition.

Modularity measures the quality of a division of a network into modules (communities). High modularity indicates that the community structure captures significant structural patterns in the graph.

Range: [-0.5, 1.0]. Values > 0.3 indicate significant community structure.

Examples

iex> graph = Yog.undirected()
...> |> Yog.add_node(1, nil)
...> |> Yog.add_node(2, nil)
...> |> Yog.add_edge_ensure(from: 1, to: 2, with: 1)
iex> communities = %{assignments: %{1 => 0, 2 => 0}, num_communities: 1}
iex> q = Yog.Community.Metrics.modularity(graph, communities)
iex> is_float(q)
true

@spec nmi(%{required(Yog.node_id()) => integer()}, %{
  required(Yog.node_id()) => integer()
}) :: float()

Computes the Normalized Mutual Information (NMI) between two partitions.

NMI measures the agreement between two community assignments, normalized by the arithmetic mean of their entropies. Range: [0, 1], where 1 means perfect agreement.

Examples

iex> truth = %{1 => 0, 2 => 0, 3 => 1, 4 => 1}
iex> detected = %{1 => 0, 2 => 0, 3 => 1, 4 => 1}
iex> Yog.Community.Metrics.nmi(detected, truth)
1.0

@spec transitivity(Yog.graph()) :: float()

Calculates the transitivity (global clustering coefficient) of the graph.

Formula: T = 3 × number_of_triangles / number_of_connected_triples

@spec triangles_per_node(Yog.graph()) :: %{required(Yog.node_id()) => integer()}

Returns the number of triangles each node participates in.

Examples

iex> graph = Yog.undirected()
...> |> Yog.add_node(1, nil) |> Yog.add_node(2, nil) |> Yog.add_node(3, nil)
...> |> Yog.add_edge_ensure(from: 1, to: 2, with: 1)
...> |> Yog.add_edge_ensure(from: 2, to: 3, with: 1)
...> |> Yog.add_edge_ensure(from: 3, to: 1, with: 1)
iex> Yog.Community.Metrics.triangles_per_node(graph)
%{1 => 1, 2 => 1, 3 => 1}