Graph Algorithms

// Simple shortest path
MATCH path = SHORTEST (a:Person {name: 'Alice'})-[:KNOWS*]->(b:Person {name: 'Bob'})
RETURN path

// Weighted shortest path with relationship properties
MATCH path = SHORTEST (a:City {name: 'NYC'})-[r:ROAD*]-(b:City {name: 'SF'})
WHERE ALL(rel IN r WHERE rel.distance IS NOT NULL)
RETURN path, REDUCE(total = 0, rel IN r | total + rel.distance) AS total_distance

// Find all paths up to length 5
MATCH path = (start:Node {id: 1})-[*1..5]->(end:Node {id: 100})
RETURN path, LENGTH(path) AS path_length
ORDER BY path_length

// Weighted path with heuristic
MATCH path = (start:Location)-[r:CONNECTED*]-(goal:Location)
WHERE start.name = 'Start' AND goal.name = 'Goal'
WITH path,
     REDUCE(cost = 0, rel IN r | cost + rel.weight) AS total_cost,
     LENGTH(path) AS hops
ORDER BY total_cost + hops * 10  // A* heuristic: cost + estimated remaining
LIMIT 1
RETURN path, total_cost

// Out-degree centrality (influence)
MATCH (u:User)-[r:FOLLOWS]->()
RETURN u.name, COUNT(r) AS followers
ORDER BY followers DESC
LIMIT 10

// In-degree centrality (popularity)
MATCH (u:User)<-[r:FOLLOWS]-()
RETURN u.name, COUNT(r) AS following
ORDER BY following DESC
LIMIT 10

// Nodes that bridge communities
MATCH path = SHORTEST (a:Person)-[:KNOWS*]-(b:Person)
WHERE a.id < b.id  // Avoid duplicates
WITH NODES(path) AS nodes
UNWIND nodes AS node
WITH node, COUNT(*) AS times_on_shortest_path
WHERE times_on_shortest_path > 1
RETURN node.name, times_on_shortest_path
ORDER BY times_on_shortest_path DESC
LIMIT 10

# Python implementation using Geode client
from geode_client import Client

async def pagerank(client, damping=0.85, iterations=20):
    # Initialize PageRank scores
    await client.query("""
        MATCH (n:Page)
        SET n.pagerank = 1.0
    """)

    for i in range(iterations):
        # Update PageRank scores
        result, _ = await client.query("""
            MATCH (source:Page)-[:LINKS]->(target:Page)
            WITH target, source, COUNT(*) AS out_degree
            MATCH (source)-[:LINKS]->()
            WITH target, SUM(source.pagerank / out_degree) AS rank_sum
            SET target.new_pagerank = $damping * rank_sum + (1 - $damping)
            RETURN AVG(ABS(target.new_pagerank - target.pagerank)) AS delta
        """, {"damping": damping})

        # Commit new scores
        await client.query("MATCH (n:Page) SET n.pagerank = n.new_pagerank")

        if result.rows[0]['delta'] < 0.0001:
            break

    return await client.query("""
        MATCH (n:Page)
        RETURN n.url, n.pagerank
        ORDER BY n.pagerank DESC
        LIMIT 20
    """)

// Initialize labels
MATCH (n:User)
SET n.community = n.id

// Propagate (repeat multiple times)
MATCH (n:User)-[:KNOWS]-(neighbor:User)
WITH n, neighbor.community AS neighbor_label, COUNT(*) AS frequency
ORDER BY n, frequency DESC
WITH n, COLLECT(neighbor_label)[0] AS most_common
SET n.community = most_common

// Identify weakly connected components
MATCH path = (n:Node)-[*]-(m:Node)
WITH n, COLLECT(DISTINCT m.id) AS component
RETURN MIN(component) AS component_id, COUNT(*) AS size
ORDER BY size DESC

// Find triangles in social network
MATCH (a:User)-[:KNOWS]->(b:User)-[:KNOWS]->(c:User)-[:KNOWS]->(a)
WHERE a.id < b.id AND b.id < c.id  // Avoid duplicates
RETURN COUNT(*) AS triangle_count

// Clustering coefficient per node
MATCH (u:User)-[:KNOWS]-(neighbor:User)
WITH u, COLLECT(DISTINCT neighbor) AS neighbors, COUNT(DISTINCT neighbor) AS degree
WHERE degree > 1
UNWIND neighbors AS n1
UNWIND neighbors AS n2
WITH u, n1, n2, degree
WHERE n1.id < n2.id
MATCH (n1)-[r:KNOWS]-(n2)
WITH u, COUNT(r) AS actual_triangles, degree * (degree - 1) / 2 AS possible_triangles
RETURN u.name, actual_triangles * 1.0 / possible_triangles AS clustering_coefficient
ORDER BY clustering_coefficient DESC

// Find similar users by common interests
MATCH (u1:User {id: 123})-[:LIKES]->(item:Item)<-[:LIKES]-(u2:User)
WHERE u1.id <> u2.id
WITH u1, u2, COUNT(DISTINCT item) AS common_interests
MATCH (u1)-[:LIKES]->(item1:Item)
WITH u1, u2, common_interests, COUNT(DISTINCT item1) AS u1_interests
MATCH (u2)-[:LIKES]->(item2:Item)
WITH u1, u2, common_interests, u1_interests, COUNT(DISTINCT item2) AS u2_interests
WITH u1, u2,
     common_interests * 1.0 / (u1_interests + u2_interests - common_interests) AS jaccard
WHERE jaccard > 0.3
RETURN u2.name, jaccard
ORDER BY jaccard DESC
LIMIT 10

# Python implementation with embeddings
async def cosine_similarity(client, user_id, limit=10):
    result, _ = await client.query("""
        MATCH (u1:User {id: $user_id})
        MATCH (u2:User) WHERE u2.id <> $user_id
        WITH u1, u2,
             REDUCE(dot = 0.0, i IN RANGE(0, SIZE(u1.embedding) - 1) |
                    dot + u1.embedding[i] * u2.embedding[i]) AS dot_product,
             SQRT(REDUCE(norm1 = 0.0, val IN u1.embedding | norm1 + val * val)) AS norm1,
             SQRT(REDUCE(norm2 = 0.0, val IN u2.embedding | norm2 + val * val)) AS norm2
        WITH u2, dot_product / (norm1 * norm2) AS similarity
        WHERE similarity > 0.5
        RETURN u2.name, similarity
        ORDER BY similarity DESC
        LIMIT $limit
    """, {"user_id": user_id, "limit": limit})
    return result

// Go implementation: iterative belief propagation
func beliefPropagation(db *sql.DB, iterations int) error {
    for i := 0; i < iterations; i++ {
        _, err := db.Exec(`
            MATCH (n:Node)-[r:EDGE]-(m:Node)
            WITH n, AVG(m.belief) AS avg_belief
            SET n.new_belief = 0.5 * n.prior + 0.5 * avg_belief
        `)
        if err != nil {
            return err
        }

        _, err = db.Exec(`MATCH (n:Node) SET n.belief = n.new_belief`)
        if err != nil {
            return err
        }
    }
    return nil
}

// Recursive category hierarchy traversal
MATCH path = (root:Category {name: 'Electronics'})-[:SUBCATEGORY*]->(leaf:Category)
WHERE NOT EXISTS { MATCH (leaf)-[:SUBCATEGORY]->() }
RETURN leaf.name, LENGTH(path) AS depth
ORDER BY depth DESC

// Rust: parallel centrality computation
use tokio::task::JoinSet;

async fn parallel_centrality(client: &GeodeClient, node_ids: Vec<i64>) -> Result<Vec<f64>> {
    let mut tasks = JoinSet::new();

    for node_id in node_ids {
        let client = client.clone();
        tasks.spawn(async move {
            let result = client.query(&format!(
                "MATCH (n {{id: {}}})-[r]->() RETURN COUNT(r) AS degree",
                node_id
            )).await?;
            Ok::<_, Error>(result[0]["degree"].as_f64().unwrap_or(0.0))
        });
    }

    let mut centralities = Vec::new();
    while let Some(result) = tasks.join_next().await {
        centralities.push(result??);
    }
    Ok(centralities)
}

// Optimize by limiting depth and filtering early
MATCH path = (start:User {id: $id})-[:KNOWS*1..4]-(end:User)
WHERE end.active = true  // Filter early
WITH path, LENGTH(path) AS depth
WHERE depth <= 3  // Limit depth
RETURN end.name, depth
ORDER BY depth
LIMIT 100

class GraphAlgorithms:
    def __init__(self, client):
        self.client = client

    async def detect_cycles(self, start_node_id):
        """Detect cycles using depth-first search"""
        visited = set()
        stack = set()
        cycles = []

        async def dfs(node_id, path):
            if node_id in stack:
                cycles.append(path + [node_id])
                return
            if node_id in visited:
                return

            visited.add(node_id)
            stack.add(node_id)

            result = await self.client.query("""
                MATCH (n {id: $id})-[:EDGE]->(m)
                RETURN m.id AS next_id
            """, {"id": node_id})

            for row in result.rows:
                await dfs(row['next_id'], path + [node_id])

            stack.remove(node_id)

        await dfs(start_node_id, [])
        return cycles

// Identify influencers
MATCH (u:User)
OPTIONAL MATCH (u)<-[:FOLLOWS]-(follower:User)
WITH u, COUNT(follower) AS followers
OPTIONAL MATCH (u)-[:POSTED]->(p:Post)<-[:LIKED]-(liker:User)
WITH u, followers, COUNT(DISTINCT liker) AS total_likes
RETURN u.name, followers, total_likes, (followers + total_likes * 0.5) AS influence_score
ORDER BY influence_score DESC
LIMIT 20

// Detect suspicious transaction rings
MATCH path = (a:Account)-[:TRANSFERRED*3..6]->(a)
WHERE ALL(r IN relationships(path) WHERE r.amount > 10000)
WITH path, REDUCE(total = 0, r IN relationships(path) | total + r.amount) AS ring_total
WHERE ring_total > 100000
RETURN path, ring_total
ORDER BY ring_total DESC

// Collaborative filtering recommendations
MATCH (u:User {id: $user_id})-[:PURCHASED]->(p:Product)<-[:PURCHASED]-(similar:User)
WHERE similar.id <> $user_id
WITH similar, COUNT(p) AS common_purchases
ORDER BY common_purchases DESC
LIMIT 10
MATCH (similar)-[:PURCHASED]->(recommendation:Product)
WHERE NOT EXISTS {
    MATCH (u:User {id: $user_id})-[:PURCHASED]->(recommendation)
}
WITH recommendation, COUNT(similar) AS recommender_count
RETURN recommendation.name, recommender_count
ORDER BY recommender_count DESC
LIMIT 5

async def k_shortest_paths(client, start_id, end_id, k=5):
    """Find k shortest paths between nodes using Yen's algorithm"""
    paths = []

    # Find first shortest path
    result, _ = await client.query("""
        MATCH path = shortestPath((start {id: $start})-[*]-(end {id: $end}))
        RETURN path
    """, {"start": start_id, "end": end_id})

    if not result:
        return paths

    paths.append(result.rows[0]['path'])

    # Find k-1 additional paths
    for _ in range(k - 1):
        candidates = []

        # For each spur node in previous path
        for i in range(len(paths[-1].nodes) - 1):
            # Remove edges from previous paths
            # Find detour through remaining graph
            # Add to candidates

            pass  # Implementation details

        if not candidates:
            break

        # Add best candidate to paths
        paths.append(min(candidates, key=lambda p: path_cost(p)))

    return paths

-- Search from both ends simultaneously
MATCH forward = (start {id: $start})-[*1..10]->(mid)
MATCH backward = (end {id: $end})-[*1..10]->(mid)
WHERE start.id <> end.id
RETURN forward + backward AS complete_path,
       length(forward) + length(backward) AS total_length
ORDER BY total_length
LIMIT 1

-- Path through specific node types
MATCH path = (start:Airport {code: 'SFO'})-[:FLIGHT*]-(end:Airport {code: 'JFK'})
WHERE ALL(node IN nodes(path) WHERE node:Airport OR node:Hub)
  AND NONE(rel IN relationships(path) WHERE rel.canceled = true)
RETURN path,
       REDUCE(cost = 0, rel IN relationships(path) | cost + rel.price) AS total_cost
ORDER BY total_cost
LIMIT 1

-- Time-constrained paths
MATCH path = (start:Station)-[:ROUTE*]->(end:Station)
WHERE start.name = 'Downtown' AND end.name = 'Airport'
  AND REDUCE(time = 0, rel IN relationships(path) | time + rel.travel_minutes) <= 60
RETURN path
ORDER BY length(path)
LIMIT 1

import numpy as np

async def eigenvector_centrality(client, iterations=100, tolerance=1e-6):
    """Compute eigenvector centrality using power iteration"""

    # Get adjacency matrix
    nodes, _ = await client.query("MATCH (n) RETURN n.id AS id ORDER BY id")
    node_ids = [row['id'] for row in nodes]
    n = len(node_ids)
    id_to_index = {node_id: i for i, node_id in enumerate(node_ids)}

    # Build adjacency matrix
    adj = np.zeros((n, n))
    edges, _ = await client.query("""
        MATCH (a)-[:CONNECTED]->(b)
        RETURN a.id AS source, b.id AS target
    """)

    for edge in edges:
        i = id_to_index[edge['source']]
        j = id_to_index[edge['target']]
        adj[i][j] = 1

    # Power iteration
    x = np.ones(n) / n
    for _ in range(iterations):
        x_new = adj @ x
        x_new = x_new / np.linalg.norm(x_new)

        if np.linalg.norm(x_new - x) < tolerance:
            break

        x = x_new

    # Store results back
    for node_id, score in zip(node_ids, x):
        await client.execute("""
            MATCH (n {id: $id})
            SET n.eigenvector_centrality = $score
        """, {"id": node_id, "score": float(score)})

    return dict(zip(node_ids, x))

-- Average shortest path length from each node
MATCH (source:Person)
MATCH (target:Person)
WHERE source.id <> target.id
WITH source,
     REDUCE(total = 0, path IN
            COLLECT(shortestPath((source)-[*]-(target))) |
            total + length(path)) AS sum_distances,
     COUNT(target) AS target_count
WITH source,
     (target_count - 1) / sum_distances AS closeness
RETURN source.name, closeness
ORDER BY closeness DESC
LIMIT 10

-- Sum of reciprocal distances
MATCH (source:Person)
OPTIONAL MATCH path = shortestPath((source)-[*]-(target:Person))
WHERE source.id <> target.id
WITH source,
     SUM(1.0 / length(path)) AS harmonic_centrality
RETURN source.name, harmonic_centrality
ORDER BY harmonic_centrality DESC

async def louvain_algorithm(client, resolution=1.0):
    """Louvain community detection algorithm"""

    # Phase 1: Assign each node to own community
    await client.execute("""
        MATCH (n)
        SET n.community = n.id
    """)

    improved = True
    iteration = 0

    while improved and iteration < 100:
        improved = False
        iteration += 1

        # For each node, try moving to neighbor's community
        nodes, _ = await client.query("MATCH (n) RETURN n.id AS id")

        for node in nodes:
            node_id = node['id']

            # Get current modularity
            current_modularity = await compute_modularity(client)

            # Try each neighbor's community
            neighbors, _ = await client.query("""
                MATCH (n {id: $id})-[:CONNECTED]-(neighbor)
                RETURN DISTINCT neighbor.community AS community
            """, {"id": node_id})

            best_community = None
            best_modularity = current_modularity

            for neighbor in neighbors:
                # Try moving to this community
                test_modularity = await test_community_move(
                    client, node_id, neighbor['community']
                )

                if test_modularity > best_modularity:
                    best_modularity = test_modularity
                    best_community = neighbor['community']

            # Move to best community if improvement found
            if best_community is not None:
                await client.execute("""
                    MATCH (n {id: $id})
                    SET n.community = $community
                """, {"id": node_id, "community": best_community})
                improved = True

        # Phase 2: Build super-graph of communities
        if not improved:
            await build_community_graph(client)

    return await get_community_assignments(client)

-- Iteratively remove edges with highest betweenness
MATCH path = allShortestPaths((a:Node)-[*]-(b:Node))
WHERE a.id < b.id
UNWIND relationships(path) AS edge
WITH edge, COUNT(*) AS betweenness
ORDER BY betweenness DESC
LIMIT 1
DELETE edge

-- Repeat until desired number of communities reached

async def tarjan_scc(client):
    """Tarjan's algorithm for strongly connected components"""

    # Get all nodes
    nodes, _ = await client.query("MATCH (n) RETURN n.id AS id")
    node_list = [n['id'] for n in nodes]

    index = 0
    stack = []
    indices = {}
    lowlinks = {}
    on_stack = set()
    sccs = []

    async def strongconnect(node_id):
        nonlocal index

        indices[node_id] = index
        lowlinks[node_id] = index
        index += 1
        stack.append(node_id)
        on_stack.add(node_id)

        # Get successors
        successors, _ = await client.query("""
            MATCH (n {id: $id})-[:EDGE]->(successor)
            RETURN successor.id AS id
        """, {"id": node_id})

        for succ in successors:
            succ_id = succ['id']

            if succ_id not in indices:
                await strongconnect(succ_id)
                lowlinks[node_id] = min(lowlinks[node_id], lowlinks[succ_id])
            elif succ_id in on_stack:
                lowlinks[node_id] = min(lowlinks[node_id], indices[succ_id])

        # Root of SCC
        if lowlinks[node_id] == indices[node_id]:
            scc = []
            while True:
                w = stack.pop()
                on_stack.remove(w)
                scc.append(w)
                if w == node_id:
                    break
            sccs.append(scc)

    for node_id in node_list:
        if node_id not in indices:
            await strongconnect(node_id)

    return sccs

async def simrank(client, decay=0.8, max_iterations=10):
    """SimRank similarity algorithm"""

    nodes, _ = await client.query("MATCH (n) RETURN n.id AS id")
    node_list = [n['id'] for n in nodes]
    n = len(node_list)

    # Initialize similarity matrix
    sim = {(a, b): 1.0 if a == b else 0.0
           for a in node_list for b in node_list}

    for iteration in range(max_iterations):
        sim_new = {}

        for a in node_list:
            for b in node_list:
                if a == b:
                    sim_new[(a, b)] = 1.0
                    continue

                # Get in-neighbors
                a_in = await get_in_neighbors(client, a)
                b_in = await get_in_neighbors(client, b)

                if not a_in or not b_in:
                    sim_new[(a, b)] = 0.0
                    continue

                # Compute similarity
                total = sum(sim[(i, j)] for i in a_in for j in b_in)
                sim_new[(a, b)] = (decay / (len(a_in) * len(b_in))) * total

        sim = sim_new

    # Store similarities
    for (a, b), score in sim.items():
        if a < b and score > 0.1:  # Store only significant similarities
            await client.execute("""
                MATCH (a {id: $a}), (b {id: $b})
                MERGE (a)-[s:SIMILAR_TO]->(b)
                SET s.simrank_score = $score
            """, {"a": a, "b": b, "score": score})

    return sim

-- Predict future links
MATCH (a:User {id: $user_id})
MATCH (a)-[:KNOWS]-(mutual)-[:KNOWS]-(b:User)
WHERE a.id <> b.id
  AND NOT EXISTS { MATCH (a)-[:KNOWS]-(b) }
WITH b, COUNT(DISTINCT mutual) AS mutual_friends,
     SUM(1.0 / log(COUNT{ MATCH (mutual)-[:KNOWS]-() })) AS aa_score
RETURN b.name, mutual_friends, aa_score
ORDER BY aa_score DESC
LIMIT 10

from node2vec import Node2Vec
import networkx as nx

async def generate_embeddings(client, dimensions=128):
    """Generate node embeddings using node2vec"""

    # Export graph to NetworkX
    G = nx.Graph()

    nodes, _ = await client.query("MATCH (n) RETURN n.id AS id")
    for node in nodes:
        G.add_node(node['id'])

    edges, _ = await client.query("""
        MATCH (a)-[:CONNECTED]-(b)
        RETURN a.id AS source, b.id AS target
    """)
    for edge in edges:
        G.add_edge(edge['source'], edge['target'])

    # Generate embeddings
    node2vec = Node2Vec(G, dimensions=dimensions, walk_length=30, num_walks=200)
    model = node2vec.fit(window=10, min_count=1, batch_words=4)

    # Store embeddings back
    for node_id in G.nodes():
        embedding = model.wv[node_id].tolist()
        await client.execute("""
            MATCH (n {id: $id})
            SET n.embedding = $embedding
        """, {"id": node_id, "embedding": embedding})

    return model

import torch
import torch_geometric

async def train_gnn_classifier(client, num_classes, hidden_channels=64):
    """Train GNN for node classification"""

    # Load graph data
    data = await load_graph_data(client)

    class GCN(torch.nn.Module):
        def __init__(self):
            super().__init__()
            self.conv1 = GCNConv(data.num_features, hidden_channels)
            self.conv2 = GCNConv(hidden_channels, num_classes)

        def forward(self, x, edge_index):
            x = self.conv1(x, edge_index)
            x = x.relu()
            x = F.dropout(x, p=0.5, training=self.training)
            x = self.conv2(x, edge_index)
            return x

    model = GCN()
    optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
    criterion = torch.nn.CrossEntropyLoss()

    # Training loop
    model.train()
    for epoch in range(200):
        optimizer.zero_grad()
        out = model(data.x, data.edge_index)
        loss = criterion(out[data.train_mask], data.y[data.train_mask])
        loss.backward()
        optimizer.step()

    # Store predictions
    model.eval()
    pred = model(data.x, data.edge_index).argmax(dim=1)

    for node_id, prediction in zip(data.node_ids, pred):
        await client.execute("""
            MATCH (n {id: $id})
            SET n.predicted_class = $class
        """, {"id": node_id, "class": int(prediction)})

    return model

import asyncio
from concurrent.futures import ThreadPoolExecutor

async def parallel_centrality_computation(client, node_ids):
    """Compute centrality for nodes in parallel"""

    async def compute_node_centrality(node_id):
        result, _ = await client.query("""
            MATCH (n {id: $id})-[r]-()
            RETURN COUNT(r) AS degree
        """, {"id": node_id})
        return node_id, result.rows[0]['degree']

    # Create tasks for all nodes
    tasks = [compute_node_centrality(nid) for nid in node_ids]

    # Execute in parallel (limited concurrency)
    semaphore = asyncio.Semaphore(50)

    async def bounded_task(task):
        async with semaphore:
            return await task

    results = await asyncio.gather(*[bounded_task(t) for t in tasks])

    return dict(results)

-- Approximate PageRank with sampling
MATCH (n:Node)
WITH n, rand() AS random
WHERE random < 0.1  // Sample 10% of nodes
MATCH (n)-[:CONNECTED*1..5]-(connected)
WITH n, COUNT(DISTINCT connected) AS approx_reach
RETURN n.id, approx_reach
ORDER BY approx_reach DESC
LIMIT 100

async def incremental_pagerank(client, new_edge):
    """Update PageRank incrementally after edge addition"""

    # Only recompute affected nodes
    affected, _ = await client.query("""
        MATCH path = (source {id: $source})-[:CONNECTED*0..2]-(affected)
        RETURN DISTINCT affected.id AS id
    """, {"source": new_edge['source']})

    # Recompute only affected subgraph
    for node in affected:
        await update_pagerank_for_node(client, node['id'])

import time

async def profile_algorithm(algorithm_func, *args, **kwargs):
    """Profile algorithm execution"""

    start_time = time.time()
    start_memory = get_memory_usage()

    result = await algorithm_func(*args, **kwargs)

    end_time = time.time()
    end_memory = get_memory_usage()

    print(f"Execution time: {end_time - start_time:.2f}s")
    print(f"Memory used: {end_memory - start_memory:.2f}MB")
    print(f"Results: {len(result.rows)} items")

    return result

import matplotlib.pyplot as plt
import networkx as nx

async def visualize_communities(client):
    """Visualize community detection results"""

    G = nx.Graph()

    # Load graph with community labels
    edges, _ = await client.query("""
        MATCH (a)-[:CONNECTED]-(b)
        RETURN a.id AS source, b.id AS target,
               a.community AS comm_a, b.community AS comm_b
    """)

    for edge in edges:
        G.add_edge(edge['source'], edge['target'])

    # Color by community
    communities, _ = await client.query("""
        MATCH (n)
        RETURN n.id AS id, n.community AS community
    """)

    community_map = {n['id']: n['community'] for n in communities}
    colors = [community_map[node] for node in G.nodes()]

    # Draw
    pos = nx.spring_layout(G)
    nx.draw(G, pos, node_color=colors, with_labels=True, cmap=plt.cm.rainbow)
    plt.savefig('communities.png')