diff --git a/java/server/src/main/java/org/softwareheritage/graph/Entry.java b/java/server/src/main/java/org/softwareheritage/graph/Entry.java
index c666333..2186d6d 100644
--- a/java/server/src/main/java/org/softwareheritage/graph/Entry.java
+++ b/java/server/src/main/java/org/softwareheritage/graph/Entry.java
@@ -1,139 +1,163 @@
 package org.softwareheritage.graph;
 
 import java.util.ArrayList;
-import java.util.Map;
 import java.io.DataOutputStream;
 import java.io.FileOutputStream;
 import java.io.IOException;
 
 import com.fasterxml.jackson.databind.ObjectMapper;
 import com.fasterxml.jackson.databind.PropertyNamingStrategy;
-import py4j.GatewayServer;
+import org.softwareheritage.graph.algo.NodeIdConsumer;
 
-import org.softwareheritage.graph.Graph;
-import org.softwareheritage.graph.Node;
 import org.softwareheritage.graph.algo.Stats;
-import org.softwareheritage.graph.algo.NodeIdsConsumer;
 import org.softwareheritage.graph.algo.Traversal;
 
 public class Entry {
-    Graph graph;
+    private Graph graph;
 
-    final long PATH_SEPARATOR_ID = -1;
+    private final long PATH_SEPARATOR_ID = -1;
 
     public void load_graph(String graphBasename) throws IOException {
         System.err.println("Loading graph " + graphBasename + " ...");
         this.graph = new Graph(graphBasename);
         System.err.println("Graph loaded.");
     }
 
+    public Graph get_graph() {
+        return graph.copy();
+    }
+
     public String stats() {
         try {
             Stats stats = new Stats(graph.getPath());
             ObjectMapper objectMapper = new ObjectMapper();
             objectMapper.setPropertyNamingStrategy(PropertyNamingStrategy.SNAKE_CASE);
-            String res = objectMapper.writeValueAsString(stats);
-            return res;
+            return objectMapper.writeValueAsString(stats);
         } catch (IOException e) {
             throw new RuntimeException("Cannot read stats: " + e);
         }
     }
 
+    private interface NodeCountVisitor {
+        void accept(long nodeId, NodeIdConsumer consumer);
+    }
+
+    private int count_visitor(NodeCountVisitor f, long srcNodeId) {
+        int count[] = { 0 };
+        f.accept(srcNodeId, (node) -> { count[0]++; });
+        return count[0];
+    }
+
+    public int count_leaves(String direction, String edgesFmt, long srcNodeId) {
+        Traversal t = new Traversal(this.graph, direction, edgesFmt);
+        return count_visitor(t::leavesVisitor, srcNodeId);
+    }
+
+    public int count_neighbors(String direction, String edgesFmt, long srcNodeId) {
+        Traversal t = new Traversal(this.graph, direction, edgesFmt);
+        return count_visitor(t::neighborsVisitor, srcNodeId);
+    }
+
+    public int count_visit_nodes(String direction, String edgesFmt, long srcNodeId) {
+        Traversal t = new Traversal(this.graph, direction, edgesFmt);
+        return count_visitor(t::visitNodesVisitor, srcNodeId);
+    }
+
     public QueryHandler get_handler(String clientFIFO) {
         return new QueryHandler(this.graph.copy(), clientFIFO);
     }
 
     public class QueryHandler {
         Graph graph;
         DataOutputStream out;
         String clientFIFO;
 
         public QueryHandler(Graph graph, String clientFIFO) {
             this.graph = graph;
             this.clientFIFO = clientFIFO;
             this.out = null;
         }
 
         public void writeNode(long nodeId) {
             try {
                 out.writeLong(nodeId);
             } catch (IOException e) {
                 throw new RuntimeException("Cannot write response to client: " + e);
             }
         }
 
         public void writePath(ArrayList<Long> path) {
             for (Long nodeId : path) {
                 writeNode(nodeId);
             }
             writeNode(PATH_SEPARATOR_ID);
         }
 
         public void open() {
             try {
                 FileOutputStream file = new FileOutputStream(this.clientFIFO);
                 this.out = new DataOutputStream(file);
             } catch (IOException e) {
                 throw new RuntimeException("Cannot open client FIFO: " + e);
             }
         }
 
         public void close() {
             try {
                 out.close();
             } catch (IOException e) {
                 throw new RuntimeException("Cannot write response to client: " + e);
             }
         }
 
         public void leaves(String direction, String edgesFmt, long srcNodeId) {
             open();
             Traversal t = new Traversal(this.graph, direction, edgesFmt);
             t.leavesVisitor(srcNodeId, this::writeNode);
             close();
         }
 
         public void neighbors(String direction, String edgesFmt, long srcNodeId) {
             open();
             Traversal t = new Traversal(this.graph, direction, edgesFmt);
             t.neighborsVisitor(srcNodeId, this::writeNode);
             close();
         }
 
         public void visit_nodes(String direction, String edgesFmt, long srcNodeId) {
             open();
             Traversal t = new Traversal(this.graph, direction, edgesFmt);
             t.visitNodesVisitor(srcNodeId, this::writeNode);
             close();
         }
 
         public void visit_paths(String direction, String edgesFmt,
                                 long srcNodeId) {
             open();
             Traversal t = new Traversal(this.graph, direction, edgesFmt);
             t.visitPathsVisitor(srcNodeId, this::writePath);
             close();
         }
 
         public void walk(String direction, String edgesFmt, String algorithm,
                          long srcNodeId, long dstNodeId) {
             open();
             Traversal t = new Traversal(this.graph, direction, edgesFmt);
             for (Long nodeId : t.walk(srcNodeId, dstNodeId, algorithm)) {
                 writeNode(nodeId);
             }
             close();
         }
 
         public void walk_type(String direction, String edgesFmt, String algorithm,
                               long srcNodeId, String dst) {
             open();
             Node.Type dstType = Node.Type.fromStr(dst);
             Traversal t = new Traversal(this.graph, direction, edgesFmt);
             for (Long nodeId : t.walk(srcNodeId, dstType, algorithm)) {
                 writeNode(nodeId);
             }
             close();
         }
     }
 }
diff --git a/swh/graph/server/backend.py b/swh/graph/backend.py
similarity index 67%
rename from swh/graph/server/backend.py
rename to swh/graph/backend.py
index 0aecc14..6d64eec 100644
--- a/swh/graph/server/backend.py
+++ b/swh/graph/backend.py
@@ -1,161 +1,186 @@
 # Copyright (C) 2019  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
 import asyncio
 import contextlib
-import json
+import io
 import os
 import pathlib
 import struct
+import subprocess
 import sys
 import tempfile
 
 from py4j.java_gateway import JavaGateway
 
 from swh.graph.pid import IntToPidMap, PidToIntMap
 from swh.model.identifiers import PID_TYPES
 
 BUF_SIZE = 64*1024
 BIN_FMT = '>q'  # 64 bit integer, big endian
 PATH_SEPARATOR_ID = -1
 NODE2PID_EXT = 'node2pid.bin'
 PID2NODE_EXT = 'pid2node.bin'
 
 
 def find_graph_jar():
-    swh_graph_root = pathlib.Path(__file__).parents[3]
+    swh_graph_root = pathlib.Path(__file__).parents[2]
     try_paths = [
         swh_graph_root / 'java/server/target/',
         pathlib.Path(sys.prefix) / 'share/swh-graph/',
     ]
     for path in try_paths:
         glob = list(path.glob('swh-graph-*.jar'))
         if glob:
             return str(glob[0])
     raise RuntimeError("swh-graph-*.jar not found. Have you run `make java`?")
 
 
+def _get_pipe_stderr():
+    # Get stderr if possible, or pipe to stdout if running with Jupyter.
+    try:
+        sys.stderr.fileno()
+    except io.UnsupportedOperation:
+        return subprocess.STDOUT
+    else:
+        return sys.stderr
+
+
 class Backend:
     def __init__(self, graph_path):
         self.gateway = None
         self.entry = None
         self.graph_path = graph_path
 
     def __enter__(self):
         self.gateway = JavaGateway.launch_gateway(
             java_path=None,
             classpath=find_graph_jar(),
             die_on_exit=True,
             redirect_stdout=sys.stdout,
-            redirect_stderr=sys.stderr,
+            redirect_stderr=_get_pipe_stderr(),
         )
         self.entry = self.gateway.jvm.org.softwareheritage.graph.Entry()
         self.entry.load_graph(self.graph_path)
         self.node2pid = IntToPidMap(self.graph_path + '.' + NODE2PID_EXT)
         self.pid2node = PidToIntMap(self.graph_path + '.' + PID2NODE_EXT)
         self.stream_proxy = JavaStreamProxy(self.entry)
+        return self
 
     def __exit__(self, exc_type, exc_value, tb):
         self.gateway.shutdown()
 
     def stats(self):
         return self.entry.stats()
 
+    def count(self, ttype, direction, edges_fmt, src):
+        method = getattr(self.entry, 'count_' + ttype)
+        return method(direction, edges_fmt, src)
+
     async def simple_traversal(self, ttype, direction, edges_fmt, src):
-        assert ttype in ('leaves', 'neighbors', 'visit_nodes', 'visit_paths')
-        src_id = self.pid2node[src]
+        assert ttype in ('leaves', 'neighbors', 'visit_nodes')
         method = getattr(self.stream_proxy, ttype)
-        async for node_id in method(direction, edges_fmt, src_id):
-            if node_id == PATH_SEPARATOR_ID:
-                yield None
-            else:
-                yield self.node2pid[node_id]
+        async for node_id in method(direction, edges_fmt, src):
+            yield node_id
 
     async def walk(self, direction, edges_fmt, algo, src, dst):
-        src_id = self.pid2node[src]
         if dst in PID_TYPES:
             it = self.stream_proxy.walk_type(direction, edges_fmt, algo,
-                                             src_id, dst)
+                                             src, dst)
         else:
-            dst_id = self.pid2node[dst]
             it = self.stream_proxy.walk(direction, edges_fmt, algo,
-                                        src_id, dst_id)
-
+                                        src, dst)
         async for node_id in it:
-            yield self.node2pid[node_id]
-
-    async def visit_paths(self, *args):
-        buffer = []
-        async for res_pid in self.simple_traversal('visit_paths', *args):
-            if res_pid is None:  # Path separator, flush
-                yield json.dumps(buffer)
-                buffer = []
+            yield node_id
+
+    async def visit_paths(self, direction, edges_fmt, src):
+        path = []
+        async for node in self.stream_proxy.visit_paths(
+                direction, edges_fmt, src):
+            if node == PATH_SEPARATOR_ID:
+                yield path
+                path = []
             else:
-                buffer.append(res_pid)
+                path.append(node)
 
 
 class JavaStreamProxy:
     """A proxy class for the org.softwareheritage.graph.Entry Java class that
     takes care of the setup and teardown of the named-pipe FIFO communication
     between Python and Java.
 
     Initialize JavaStreamProxy using:
 
         proxy = JavaStreamProxy(swh_entry_class_instance)
 
     Then you can call an Entry method and iterate on the FIFO results like
     this:
 
         async for value in proxy.java_method(arg1, arg2):
             print(value)
     """
 
     def __init__(self, entry):
         self.entry = entry
 
     async def read_node_ids(self, fname):
         loop = asyncio.get_event_loop()
-        with (await loop.run_in_executor(None, open, fname, 'rb')) as f:
+        open_thread = loop.run_in_executor(None, open, fname, 'rb')
+
+        # Since the open() call on the FIFO is blocking until it is also opened
+        # on the Java side, we await it with a timeout in case there is an
+        # exception that prevents the write-side open().
+        with (await asyncio.wait_for(open_thread, timeout=2)) as f:
             while True:
                 data = await loop.run_in_executor(None, f.read, BUF_SIZE)
                 if not data:
                     break
                 for data in struct.iter_unpack(BIN_FMT, data):
                     yield data[0]
 
     class _HandlerWrapper:
         def __init__(self, handler):
             self._handler = handler
 
         def __getattr__(self, name):
             func = getattr(self._handler, name)
 
             async def java_call(*args, **kwargs):
                 loop = asyncio.get_event_loop()
                 await loop.run_in_executor(None, lambda: func(*args, **kwargs))
 
             def java_task(*args, **kwargs):
                 return asyncio.create_task(java_call(*args, **kwargs))
 
             return java_task
 
     @contextlib.contextmanager
     def get_handler(self):
         with tempfile.TemporaryDirectory(prefix='swh-graph-') as tmpdirname:
             cli_fifo = os.path.join(tmpdirname, 'swh-graph.fifo')
             os.mkfifo(cli_fifo)
             reader = self.read_node_ids(cli_fifo)
             query_handler = self.entry.get_handler(cli_fifo)
             handler = self._HandlerWrapper(query_handler)
             yield (handler, reader)
 
     def __getattr__(self, name):
         async def java_call_iterator(*args, **kwargs):
             with self.get_handler() as (handler, reader):
                 java_task = getattr(handler, name)(*args, **kwargs)
-                async for value in reader:
-                    yield value
+                try:
+                    async for value in reader:
+                        yield value
+                except asyncio.TimeoutError:
+                    # If the read-side open() timeouts, an exception on the
+                    # Java side probably happened that prevented the
+                    # write-side open(). We propagate this exception here if
+                    # that is the case.
+                    task_exc = java_task.exception()
+                    if task_exc:
+                        raise task_exc
+                    raise
                 await java_task
         return java_call_iterator
diff --git a/swh/graph/cli.py b/swh/graph/cli.py
index c0f5626..97c0ad2 100644
--- a/swh/graph/cli.py
+++ b/swh/graph/cli.py
@@ -1,150 +1,150 @@
 # Copyright (C) 2019  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
 import aiohttp
 import click
 import sys
 
 from swh.core.cli import CONTEXT_SETTINGS, AliasedGroup
 from swh.graph import client
 from swh.graph.pid import PidToIntMap, IntToPidMap
 from swh.graph.server.app import make_app
-from swh.graph.server.backend import Backend
+from swh.graph.backend import Backend
 
 
 @click.group(name='graph', context_settings=CONTEXT_SETTINGS,
              cls=AliasedGroup)
 @click.pass_context
 def cli(ctx):
     """Software Heritage graph tools."""
     ctx.ensure_object(dict)
 
 
 @cli.command('api-client')
 @click.option('--host', default='localhost', help='Graph server host')
 @click.option('--port', default='5009', help='Graph server port')
 @click.pass_context
 def api_client(ctx, host, port):
     """Client for the Software Heritage Graph REST service
 
     """
     url = 'http://{}:{}'.format(host, port)
     app = client.RemoteGraphClient(url)
 
     # TODO: run web app
     print(app.stats())
 
 
 @cli.group('map')
 @click.pass_context
 def map(ctx):
     """Manage swh-graph on-disk maps"""
     pass
 
 
 def dump_pid2int(filename):
     for (pid, int) in PidToIntMap(filename):
         print('{}\t{}'.format(pid, int))
 
 
 def dump_int2pid(filename):
     for (int, pid) in IntToPidMap(filename):
         print('{}\t{}'.format(int, pid))
 
 
 def restore_pid2int(filename):
     """read a textual PID->int map from stdin and write its binary version to
     filename
 
     """
     with open(filename, 'wb') as dst:
         for line in sys.stdin:
             (str_pid, str_int) = line.split()
             PidToIntMap.write_record(dst, str_pid, int(str_int))
 
 
 def restore_int2pid(filename, length):
     """read a textual int->PID map from stdin and write its binary version to
     filename
 
     """
     int2pid = IntToPidMap(filename, mode='wb', length=length)
     for line in sys.stdin:
         (str_int, str_pid) = line.split()
         int2pid[int(str_int)] = str_pid
     int2pid.close()
 
 
 @map.command('dump')
 @click.option('--type', '-t', 'map_type', required=True,
               type=click.Choice(['pid2int', 'int2pid']),
               help='type of map to dump')
 @click.argument('filename', required=True, type=click.Path(exists=True))
 @click.pass_context
 def dump_map(ctx, map_type, filename):
     """dump a binary PID<->int map to textual format"""
     if map_type == 'pid2int':
         dump_pid2int(filename)
     elif map_type == 'int2pid':
         dump_int2pid(filename)
     else:
         raise ValueError('invalid map type: ' + map_type)
     pass
 
 
 @map.command('restore')
 @click.option('--type', '-t', 'map_type', required=True,
               type=click.Choice(['pid2int', 'int2pid']),
               help='type of map to dump')
 @click.option('--length', '-l', type=int,
               help='''map size in number of logical records
               (required for int2pid maps)''')
 @click.argument('filename', required=True, type=click.Path())
 @click.pass_context
 def restore_map(ctx, map_type, length, filename):
     """restore a binary PID<->int map from textual format"""
     if map_type == 'pid2int':
         restore_pid2int(filename)
     elif map_type == 'int2pid':
         if length is None:
             raise click.UsageError(
                 'map length is required when restoring {} maps'.format(
                     map_type), ctx)
         restore_int2pid(filename, length)
     else:
         raise ValueError('invalid map type: ' + map_type)
 
 
 @cli.group('graph')
 @click.pass_context
 def graph(ctx):
     """Manage swh-graph on-disk maps"""
     pass
 
 
 @graph.command(name='rpc-serve')
 @click.option('--host', default='0.0.0.0',
               metavar='IP', show_default=True,
               help="Host ip address to bind the server on")
 @click.option('--port', default=5009, type=click.INT,
               metavar='PORT', show_default=True,
               help="Binding port of the server")
 @click.option('--graph', required=True, metavar='GRAPH',
               help="Path prefix of the graph to load")
 @click.pass_context
 def serve(ctx, host, port, graph):
     backend = Backend(graph_path=graph)
     app = make_app(backend=backend)
 
     with backend:
         aiohttp.web.run_app(app, host=host, port=port)
 
 
 def main():
     return cli(auto_envvar_prefix='SWH_GRAPH')
 
 
 if __name__ == '__main__':
     main()
diff --git a/swh/graph/client.py b/swh/graph/client.py
index a2a8095..8254fe7 100644
--- a/swh/graph/client.py
+++ b/swh/graph/client.py
@@ -1,82 +1,106 @@
 # Copyright (C) 2019  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
 import json
 
 from swh.core.api import RPCClient
 
 
 class GraphAPIError(Exception):
     """Graph API Error"""
     def __str__(self):
         return ('An unexpected error occurred in the Graph backend: {}'
                 .format(self.args))
 
 
 class RemoteGraphClient(RPCClient):
     """Client to the Software Heritage Graph."""
 
     def __init__(self, url, timeout=None):
         super().__init__(
             api_exception=GraphAPIError, url=url, timeout=timeout)
 
     def raw_verb_lines(self, verb, endpoint, **kwargs):
         response = self.raw_verb(verb, endpoint, stream=True, **kwargs)
         for line in response.iter_lines():
             yield line.decode().lstrip('\n')
 
     def get_lines(self, endpoint, **kwargs):
         yield from self.raw_verb_lines('get', endpoint, **kwargs)
 
     # Web API endpoints
 
     def stats(self):
         return self.get('stats')
 
     def leaves(self, src, edges="*", direction="forward"):
         return self.get_lines(
             'leaves/{}'.format(src),
             params={
                 'edges': edges,
                 'direction': direction
             })
 
     def neighbors(self, src, edges="*", direction="forward"):
         return self.get_lines(
             'neighbors/{}'.format(src),
             params={
                 'edges': edges,
                 'direction': direction
             })
 
     def visit_nodes(self, src, edges="*", direction="forward"):
         return self.get_lines(
             'visit/nodes/{}'.format(src),
             params={
                 'edges': edges,
                 'direction': direction
             })
 
     def visit_paths(self, src, edges="*", direction="forward"):
         def decode_path_wrapper(it):
             for e in it:
                 yield json.loads(e)
 
         return decode_path_wrapper(
             self.get_lines(
                 'visit/paths/{}'.format(src),
                 params={
                     'edges': edges,
                     'direction': direction
                 }))
 
     def walk(self, src, dst, edges="*", traversal="dfs", direction="forward"):
         return self.get_lines(
             'walk/{}/{}'.format(src, dst),
             params={
                 'edges': edges,
                 'traversal': traversal,
                 'direction': direction
             })
+
+    def count_leaves(self, src, edges="*", direction="forward"):
+        return self.get(
+            'leaves/count/{}'.format(src),
+            params={
+                'edges': edges,
+                'direction': direction
+            })
+
+    def count_neighbors(self, src, edges="*", direction="forward"):
+        return self.get(
+            'neighbors/count/{}'.format(src),
+            params={
+                'edges': edges,
+                'direction': direction
+            })
+
+    def count_visit_nodes(self, src, edges="*", direction="forward"):
+        return self.get(
+            'visit/nodes/count/{}'.format(src),
+            params={
+                'edges': edges,
+                'direction': direction
+            })
diff --git a/swh/graph/dot.py b/swh/graph/dot.py
new file mode 100644
index 0000000..b2d455a
--- /dev/null
+++ b/swh/graph/dot.py
@@ -0,0 +1,65 @@
+# Copyright (C) 2019  The Software Heritage developers
+# See the AUTHORS file at the top-level directory of this distribution
+# License: GNU General Public License version 3, or any later version
+# See top-level LICENSE file for more information
+
+from functools import lru_cache
+import subprocess
+import collections
+
+
+KIND_TO_SHAPE = {
+    'ori': 'egg',
+    'snp': 'doubleoctagon',
+    'rel': 'octagon',
+    'rev': 'diamond',
+    'dir': 'folder',
+    'cnt': 'oval',
+}
+
+
+@lru_cache()
+def dot_to_svg(dot):
+    try:
+        p = subprocess.run(
+            ['dot', '-Tsvg'], input=dot,
+            universal_newlines=True, capture_output=True,
+            check=True
+        )
+    except subprocess.CalledProcessError as e:
+        raise RuntimeError(e.stderr) from e
+    return p.stdout
+
+
+def graph_dot(nodes):
+    ids = {n.id for n in nodes}
+
+    by_kind = collections.defaultdict(list)
+    for n in nodes:
+        by_kind[n.kind].append(n)
+
+    forward_edges = [
+        (node.id, child.id)
+        for node in nodes
+        for child in node.children()
+        if child.id in ids
+    ]
+    backward_edges = [
+        (parent.id, node.id)
+        for node in nodes
+        for parent in node.parents()
+        if parent.id in ids
+    ]
+    edges = set(forward_edges + backward_edges)
+    edges_fmt = '\n'.join('{} -> {};'.format(a, b) for a, b in edges)
+    nodes_fmt = '\n'.join(node.dot_fragment() for node in nodes)
+
+    s = """digraph G {{
+    ranksep=1;
+    nodesep=0.5;
+
+    {nodes}
+    {edges}
+
+    }}""".format(nodes=nodes_fmt, edges=edges_fmt)
+    return s
diff --git a/swh/graph/graph.py b/swh/graph/graph.py
new file mode 100644
index 0000000..ed042d3
--- /dev/null
+++ b/swh/graph/graph.py
@@ -0,0 +1,166 @@
+# Copyright (C) 2019  The Software Heritage developers
+# See the AUTHORS file at the top-level directory of this distribution
+# License: GNU General Public License version 3, or any later version
+# See top-level LICENSE file for more information
+
+import asyncio
+import contextlib
+import functools
+from swh.graph.backend import Backend
+from swh.graph.dot import dot_to_svg, graph_dot, KIND_TO_SHAPE
+
+
+BASE_URL = 'https://archive.softwareheritage.org/browse'
+KIND_TO_URL_FRAGMENT = {
+    'ori': '/origin/{}',
+    'snp': '/snapshot/{}',
+    'rel': '/release/{}',
+    'rev': '/revision/{}',
+    'dir': '/directory/{}',
+    'cnt': '/content/sha1_git:{}/',
+}
+
+
+def call_async_gen(generator, *args, **kwargs):
+    loop = asyncio.get_event_loop()
+    it = generator(*args, **kwargs).__aiter__()
+    while True:
+        try:
+            res = loop.run_until_complete(it.__anext__())
+            yield res
+        except StopAsyncIteration:
+            break
+
+
+class Neighbors:
+    """Neighbor iterator with custom O(1) length method"""
+    def __init__(self, graph, iterator, length_func):
+        self.graph = graph
+        self.iterator = iterator
+        self.length_func = length_func
+
+    def __iter__(self):
+        return self
+
+    def __next__(self):
+        succ = self.iterator.nextLong()
+        if succ == -1:
+            raise StopIteration
+        return GraphNode(self.graph, succ)
+
+    def __len__(self):
+        return self.length_func()
+
+
+class GraphNode:
+    """Node in the SWH graph"""
+
+    def __init__(self, graph, node_id):
+        self.graph = graph
+        self.id = node_id
+
+    def children(self):
+        return Neighbors(
+            self.graph,
+            self.graph.java_graph.successors(self.id),
+            lambda: self.graph.java_graph.outdegree(self.id))
+
+    def parents(self):
+        return Neighbors(
+            self.graph,
+            self.graph.java_graph.predecessors(self.id),
+            lambda: self.graph.java_graph.indegree(self.id))
+
+    def simple_traversal(self, ttype, direction='forward', edges='*'):
+        for node in call_async_gen(
+            self.graph.backend.simple_traversal,
+            ttype, direction, edges, self.id
+        ):
+            yield self.graph[node]
+
+    def leaves(self, *args, **kwargs):
+        yield from self.simple_traversal('leaves', *args, **kwargs)
+
+    def visit_nodes(self, *args, **kwargs):
+        yield from self.simple_traversal('visit_nodes', *args, **kwargs)
+
+    def visit_paths(self, direction='forward', edges='*'):
+        for path in call_async_gen(
+                self.graph.backend.visit_paths,
+                direction, edges, self.id
+        ):
+            yield [self.graph[node] for node in path]
+
+    def walk(self, dst, direction='forward', edges='*', traversal='dfs'):
+        for node in call_async_gen(
+            self.graph.backend.walk,
+            direction, edges, traversal, self.id, dst
+        ):
+            yield self.graph[node]
+
+    def _count(self, ttype, direction='forward', edges='*'):
+        return self.graph.backend.count(ttype, direction, edges, self.id)
+
+    count_leaves = functools.partialmethod(_count, ttype='leaves')
+    count_neighbors = functools.partialmethod(_count, ttype='neighbors')
+    count_visit_nodes = functools.partialmethod(_count, ttype='visit_nodes')
+
+    @property
+    def pid(self):
+        return self.graph.node2pid[self.id]
+
+    @property
+    def kind(self):
+        return self.pid.split(':')[2]
+
+    def __str__(self):
+        return self.pid
+
+    def __repr__(self):
+        return '<{}>'.format(self.pid)
+
+    def dot_fragment(self):
+        swh, version, kind, hash = self.pid.split(':')
+        label = '{}:{}..{}'.format(kind, hash[0:2], hash[-2:])
+        url = BASE_URL + KIND_TO_URL_FRAGMENT[kind].format(hash)
+        shape = KIND_TO_SHAPE[kind]
+        return ('{} [label="{}", href="{}", target="_blank", shape="{}"];'
+                .format(self.id, label, url, shape))
+
+    def _repr_svg_(self):
+        nodes = [self, *list(self.children()), *list(self.parents())]
+        dot = graph_dot(nodes)
+        svg = dot_to_svg(dot)
+        return svg
+
+
+class Graph:
+    def __init__(self, backend, node2pid, pid2node):
+        self.backend = backend
+        self.java_graph = backend.entry.get_graph()
+        self.node2pid = node2pid
+        self.pid2node = pid2node
+
+    def stats(self):
+        return self.backend.stats()
+
+    @property
+    def path(self):
+        return self.java_graph.getPath()
+
+    def __len__(self):
+        return self.java_graph.getNbNodes()
+
+    def __getitem__(self, node_id):
+        if isinstance(node_id, int):
+            self.node2pid[node_id]  # check existence
+            return GraphNode(self, node_id)
+        elif isinstance(node_id, str):
+            node_id = self.pid2node[node_id]
+            return GraphNode(self, node_id)
+
+
+@contextlib.contextmanager
+def load(graph_path):
+    with Backend(graph_path) as backend:
+        yield Graph(backend, backend.node2pid, backend.pid2node)
diff --git a/swh/graph/server/app.py b/swh/graph/server/app.py
index 21b9dbc..c5d4759 100644
--- a/swh/graph/server/app.py
+++ b/swh/graph/server/app.py
@@ -1,102 +1,144 @@
 # Copyright (C) 2019  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
 """
 A proxy HTTP server for swh-graph, talking to the Java code via py4j, and using
 FIFO as a transport to stream integers between the two languages.
 """
 
+import json
 import contextlib
 import aiohttp.web
 
 from swh.core.api.asynchronous import RPCServerApp
+from swh.model.identifiers import PID_TYPES
 
 
 @contextlib.asynccontextmanager
 async def stream_response(request, *args, **kwargs):
     response = aiohttp.web.StreamResponse(*args, **kwargs)
     await response.prepare(request)
     yield response
     await response.write_eof()
 
 
 async def index(request):
     return aiohttp.web.Response(
         content_type='text/html',
         body="""<html>
 <head><title>Software Heritage storage server</title></head>
 <body>
 <p>You have reached the <a href="https://www.softwareheritage.org/">
 Software Heritage</a> graph API server.</p>
 
 <p>See its
 <a href="https://docs.softwareheritage.org/devel/swh-graph/api.html">API
 documentation</a> for more information.</p>
 </body>
 </html>""")
 
 
 async def stats(request):
     stats = request.app['backend'].stats()
     return aiohttp.web.Response(body=stats, content_type='application/json')
 
 
 def get_simple_traversal_handler(ttype):
     async def simple_traversal(request):
+        backend = request.app['backend']
+
         src = request.match_info['src']
         edges = request.query.get('edges', '*')
         direction = request.query.get('direction', 'forward')
 
+        src_node = backend.pid2node[src]
         async with stream_response(request) as response:
-            async for res_pid in request.app['backend'].simple_traversal(
-                ttype, direction, edges, src
+            async for res_node in backend.simple_traversal(
+                ttype, direction, edges, src_node
             ):
+                res_pid = backend.node2pid[res_node]
                 await response.write('{}\n'.format(res_pid).encode())
             return response
 
     return simple_traversal
 
 
 async def walk(request):
+    backend = request.app['backend']
+
     src = request.match_info['src']
     dst = request.match_info['dst']
     edges = request.query.get('edges', '*')
     direction = request.query.get('direction', 'forward')
     algo = request.query.get('traversal', 'dfs')
 
-    it = request.app['backend'].walk(direction, edges, algo, src, dst)
+    src_node = backend.pid2node[src]
+    if dst not in PID_TYPES:
+        dst = backend.pid2node[dst]
     async with stream_response(request) as response:
-        async for res_pid in it:
+        async for res_node in backend.walk(
+                direction, edges, algo, src_node, dst
+        ):
+            res_pid = backend.node2pid[res_node]
             await response.write('{}\n'.format(res_pid).encode())
         return response
 
 
 async def visit_paths(request):
+    backend = request.app['backend']
+
     src = request.match_info['src']
     edges = request.query.get('edges', '*')
     direction = request.query.get('direction', 'forward')
 
-    it = request.app['backend'].visit_paths(direction, edges, src)
+    src_node = backend.pid2node[src]
+    it = backend.visit_paths(direction, edges, src_node)
     async with stream_response(request) as response:
-        async for res_pid in it:
-            await response.write('{}\n'.format(res_pid).encode())
+        async for res_path in it:
+            res_path_pid = [backend.node2pid[n] for n in res_path]
+            line = json.dumps(res_path_pid)
+            await response.write('{}\n'.format(line).encode())
         return response
 
 
+def get_count_handler(ttype):
+    async def count(request):
+        backend = request.app['backend']
+
+        src = request.match_info['src']
+        edges = request.query.get('edges', '*')
+        direction = request.query.get('direction', 'forward')
+
+        src_node = backend.pid2node[src]
+        cnt = backend.count(ttype, direction, edges, src_node)
+        return aiohttp.web.Response(body=str(cnt),
+                                    content_type='application/json')
+
+    return count
+
+
 def make_app(backend, **kwargs):
     app = RPCServerApp(**kwargs)
     app.router.add_route('GET', '/', index)
     app.router.add_route('GET', '/graph/stats', stats)
+
     app.router.add_route('GET', '/graph/leaves/{src}',
                          get_simple_traversal_handler('leaves'))
     app.router.add_route('GET', '/graph/neighbors/{src}',
                          get_simple_traversal_handler('neighbors'))
     app.router.add_route('GET', '/graph/visit/nodes/{src}',
                          get_simple_traversal_handler('visit_nodes'))
     app.router.add_route('GET', '/graph/visit/paths/{src}', visit_paths)
     app.router.add_route('GET', '/graph/walk/{src}/{dst}', walk)
 
+    app.router.add_route('GET', '/graph/neighbors/count/{src}',
+                         get_count_handler('neighbors'))
+    app.router.add_route('GET', '/graph/leaves/count/{src}',
+                         get_count_handler('leaves'))
+    app.router.add_route('GET', '/graph/visit/nodes/count/{src}',
+                         get_count_handler('visit_nodes'))
+
     app['backend'] = backend
     return app
diff --git a/swh/graph/tests/conftest.py b/swh/graph/tests/conftest.py
index b6b26bc..1c391a8 100644
--- a/swh/graph/tests/conftest.py
+++ b/swh/graph/tests/conftest.py
@@ -1,39 +1,46 @@
 import multiprocessing
 import pytest
 from pathlib import Path
 
 from aiohttp.test_utils import TestServer, TestClient, loop_context
 
+from swh.graph.graph import load as graph_load
 from swh.graph.client import RemoteGraphClient
-from swh.graph.server.backend import Backend
+from swh.graph.backend import Backend
 from swh.graph.server.app import make_app
 
 SWH_GRAPH_ROOT = Path(__file__).parents[3]
 TEST_GRAPH_PATH = SWH_GRAPH_ROOT / 'tests/dataset/output/example'
 
 
 class GraphServerProcess(multiprocessing.Process):
     def __init__(self, q, *args, **kwargs):
         self.q = q
         super().__init__(*args, **kwargs)
 
     def run(self):
         backend = Backend(graph_path=str(TEST_GRAPH_PATH))
         with backend:
             with loop_context() as loop:
-                app = make_app(backend=backend)
+                app = make_app(backend=backend, debug=True)
                 client = TestClient(TestServer(app), loop=loop)
                 loop.run_until_complete(client.start_server())
                 url = client.make_url('/graph/')
                 self.q.put(url)
                 loop.run_forever()
 
 
 @pytest.fixture(scope="module")
 def graph_client():
     queue = multiprocessing.Queue()
     server = GraphServerProcess(queue)
     server.start()
     url = queue.get()
     yield RemoteGraphClient(str(url))
     server.terminate()
+
+
+@pytest.fixture(scope="module")
+def graph():
+    with graph_load(str(TEST_GRAPH_PATH)) as g:
+        yield g
diff --git a/swh/graph/tests/test_api_client.py b/swh/graph/tests/test_api_client.py
index bbf55a2..8ff3cf4 100644
--- a/swh/graph/tests/test_api_client.py
+++ b/swh/graph/tests/test_api_client.py
@@ -1,104 +1,122 @@
 def test_stats(graph_client):
     stats = graph_client.stats()
 
     assert set(stats.keys()) == {'counts', 'ratios', 'indegree',
                                  'outdegree'}
 
     assert set(stats['counts'].keys()) == {'nodes', 'edges'}
     assert set(stats['ratios'].keys()) == {'compression', 'bits_per_node',
                                            'bits_per_edge', 'avg_locality'}
     assert set(stats['indegree'].keys()) == {'min', 'max', 'avg'}
     assert set(stats['outdegree'].keys()) == {'min', 'max', 'avg'}
 
     assert stats['counts']['nodes'] == 21
     assert stats['counts']['edges'] == 23
     assert isinstance(stats['ratios']['compression'], float)
     assert isinstance(stats['ratios']['bits_per_node'], float)
     assert isinstance(stats['ratios']['bits_per_edge'], float)
     assert isinstance(stats['ratios']['avg_locality'], float)
     assert stats['indegree']['min'] == 0
     assert stats['indegree']['max'] == 3
     assert isinstance(stats['indegree']['avg'], float)
     assert stats['outdegree']['min'] == 0
     assert stats['outdegree']['max'] == 3
     assert isinstance(stats['outdegree']['avg'], float)
 
 
 def test_leaves(graph_client):
     actual = list(graph_client.leaves(
         'swh:1:ori:0000000000000000000000000000000000000021'
     ))
     expected = [
         'swh:1:cnt:0000000000000000000000000000000000000001',
         'swh:1:cnt:0000000000000000000000000000000000000004',
         'swh:1:cnt:0000000000000000000000000000000000000005',
         'swh:1:cnt:0000000000000000000000000000000000000007'
     ]
     assert set(actual) == set(expected)
 
 
 def test_neighbors(graph_client):
     actual = list(graph_client.neighbors(
         'swh:1:rev:0000000000000000000000000000000000000009',
         direction='backward'
     ))
     expected = [
         'swh:1:snp:0000000000000000000000000000000000000020',
         'swh:1:rel:0000000000000000000000000000000000000010',
         'swh:1:rev:0000000000000000000000000000000000000013'
     ]
     assert set(actual) == set(expected)
 
 
 def test_visit_nodes(graph_client):
     actual = list(graph_client.visit_nodes(
         'swh:1:rel:0000000000000000000000000000000000000010',
         edges='rel:rev,rev:rev'
     ))
     expected = [
         'swh:1:rel:0000000000000000000000000000000000000010',
         'swh:1:rev:0000000000000000000000000000000000000009',
         'swh:1:rev:0000000000000000000000000000000000000003'
     ]
     assert set(actual) == set(expected)
 
 
 def test_visit_paths(graph_client):
     actual = list(graph_client.visit_paths(
         'swh:1:snp:0000000000000000000000000000000000000020',
         edges='snp:*,rev:*'))
     actual = [tuple(path) for path in actual]
     expected = [
         (
             'swh:1:snp:0000000000000000000000000000000000000020',
             'swh:1:rev:0000000000000000000000000000000000000009',
             'swh:1:rev:0000000000000000000000000000000000000003',
             'swh:1:dir:0000000000000000000000000000000000000002'
         ),
         (
             'swh:1:snp:0000000000000000000000000000000000000020',
             'swh:1:rev:0000000000000000000000000000000000000009',
             'swh:1:dir:0000000000000000000000000000000000000008'
         ),
         (
             'swh:1:snp:0000000000000000000000000000000000000020',
             'swh:1:rel:0000000000000000000000000000000000000010'
         )
     ]
     assert set(actual) == set(expected)
 
 
 def test_walk(graph_client):
     actual = list(graph_client.walk(
         'swh:1:dir:0000000000000000000000000000000000000016', 'rel',
         edges='dir:dir,dir:rev,rev:*',
         direction='backward',
         traversal='bfs'
     ))
     expected = [
         'swh:1:dir:0000000000000000000000000000000000000016',
         'swh:1:dir:0000000000000000000000000000000000000017',
         'swh:1:rev:0000000000000000000000000000000000000018',
         'swh:1:rel:0000000000000000000000000000000000000019'
     ]
     assert set(actual) == set(expected)
+
+
+def test_count(graph_client):
+    print(graph_client)
+    actual = graph_client.count_leaves(
+        'swh:1:ori:0000000000000000000000000000000000000021'
+    )
+    assert actual == 4
+    actual = graph_client.count_visit_nodes(
+        'swh:1:rel:0000000000000000000000000000000000000010',
+        edges='rel:rev,rev:rev'
+    )
+    assert actual == 3
+    actual = graph_client.count_neighbors(
+        'swh:1:rev:0000000000000000000000000000000000000009',
+        direction='backward'
+    )
+    assert actual == 3
diff --git a/swh/graph/tests/test_graph.py b/swh/graph/tests/test_graph.py
new file mode 100644
index 0000000..4fe848d
--- /dev/null
+++ b/swh/graph/tests/test_graph.py
@@ -0,0 +1,112 @@
+import pytest
+
+
+def test_graph(graph):
+    assert len(graph) == 21
+
+    obj = 'swh:1:dir:0000000000000000000000000000000000000008'
+    node = graph[obj]
+
+    assert str(node) == obj
+    assert len(node.children()) == 3
+    assert len(node.parents()) == 2
+
+    actual = {p.pid for p in node.children()}
+    expected = {
+        'swh:1:cnt:0000000000000000000000000000000000000001',
+        'swh:1:dir:0000000000000000000000000000000000000006',
+        'swh:1:cnt:0000000000000000000000000000000000000007'
+    }
+    assert expected == actual
+
+    actual = {p.pid for p in node.parents()}
+    expected = {
+        'swh:1:rev:0000000000000000000000000000000000000009',
+        'swh:1:dir:0000000000000000000000000000000000000012',
+    }
+    assert expected == actual
+
+
+def test_invalid_pid(graph):
+    with pytest.raises(IndexError):
+        graph[1337]
+
+    with pytest.raises(IndexError):
+        graph[len(graph) + 1]
+
+    with pytest.raises(KeyError):
+        graph['swh:1:dir:0000000000000000000000000000000420000012']
+
+
+def test_leaves(graph):
+    actual = list(graph['swh:1:ori:0000000000000000000000000000000000000021']
+                  .leaves())
+    actual = [p.pid for p in actual]
+    expected = [
+        'swh:1:cnt:0000000000000000000000000000000000000001',
+        'swh:1:cnt:0000000000000000000000000000000000000004',
+        'swh:1:cnt:0000000000000000000000000000000000000005',
+        'swh:1:cnt:0000000000000000000000000000000000000007'
+    ]
+    assert set(actual) == set(expected)
+
+
+def test_visit_nodes(graph):
+    actual = list(graph['swh:1:rel:0000000000000000000000000000000000000010']
+                  .visit_nodes(edges='rel:rev,rev:rev'))
+    actual = [p.pid for p in actual]
+    expected = [
+        'swh:1:rel:0000000000000000000000000000000000000010',
+        'swh:1:rev:0000000000000000000000000000000000000009',
+        'swh:1:rev:0000000000000000000000000000000000000003'
+    ]
+    assert set(actual) == set(expected)
+
+
+def test_visit_paths(graph):
+    actual = list(graph['swh:1:snp:0000000000000000000000000000000000000020']
+                  .visit_paths(edges='snp:*,rev:*'))
+    actual = [tuple(n.pid for n in path) for path in actual]
+    expected = [
+        (
+            'swh:1:snp:0000000000000000000000000000000000000020',
+            'swh:1:rev:0000000000000000000000000000000000000009',
+            'swh:1:rev:0000000000000000000000000000000000000003',
+            'swh:1:dir:0000000000000000000000000000000000000002'
+        ),
+        (
+            'swh:1:snp:0000000000000000000000000000000000000020',
+            'swh:1:rev:0000000000000000000000000000000000000009',
+            'swh:1:dir:0000000000000000000000000000000000000008'
+        ),
+        (
+            'swh:1:snp:0000000000000000000000000000000000000020',
+            'swh:1:rel:0000000000000000000000000000000000000010'
+        )
+    ]
+    assert set(actual) == set(expected)
+
+
+def test_walk(graph):
+    actual = list(graph['swh:1:dir:0000000000000000000000000000000000000016']
+                  .walk('rel',
+                        edges='dir:dir,dir:rev,rev:*',
+                        direction='backward',
+                        traversal='bfs'))
+    actual = [p.pid for p in actual]
+    expected = [
+        'swh:1:dir:0000000000000000000000000000000000000016',
+        'swh:1:dir:0000000000000000000000000000000000000017',
+        'swh:1:rev:0000000000000000000000000000000000000018',
+        'swh:1:rel:0000000000000000000000000000000000000019'
+    ]
+    assert set(actual) == set(expected)
+
+
+def test_count(graph):
+    assert (graph['swh:1:ori:0000000000000000000000000000000000000021']
+            .count_leaves() == 4)
+    assert (graph['swh:1:rel:0000000000000000000000000000000000000010']
+            .count_visit_nodes(edges='rel:rev,rev:rev') == 3)
+    assert (graph['swh:1:rev:0000000000000000000000000000000000000009']
+            .count_neighbors(direction='backward') == 3)