diff --git a/src/storage/layout/complement.rs b/src/storage/layout/complement.rs
new file mode 100644
index 0000000..ae1c542
--- /dev/null
+++ b/src/storage/layout/complement.rs
@@ -0,0 +1,100 @@
+use std::num::NonZeroU64;
+
+use parking_lot::Mutex;
+use sprs::TriMat;
+use zarrs::array::codec::array_to_bytes::sharding::ShardingCodecBuilder;
+use zarrs::array::codec::ArrayToBytesCodecTraits;
+use zarrs::array::codec::GzipCodec;
+use zarrs::array::ChunkGrid;
+use zarrs::array::DataType;
+use zarrs::array::DimensionName;
+use zarrs::array::FillValue;
+
+use super::ChunkingStrategy;
+use super::Dimensionality;
+use super::StorageResult;
+
+use crate::io::Graph;
+use crate::storage::layout::LayoutOps;
+use crate::storage::layout::ComplementaryLayout;
+
+type Chunk = (u32, u32, u32);
+
+pub struct ComplementLayout;
+
+
+
+
+impl ComplementaryLayout<Chunk> for ComplementLayout {
+    fn shape(&self, dimensionality: &Dimensionality) -> Vec<u64> {
+        vec![dimensionality.get_graph_size(), 3]
+    }
+
+    fn data_type(&self) -> DataType {
+        DataType::UInt64
+    }
+
+    fn chunk_shape(&self, chunking_strategy: ChunkingStrategy, _: &Dimensionality) -> ChunkGrid {
+        vec![chunking_strategy.into(), NonZeroU64::new(3).unwrap()].into() // TODO: make this a constant value
+    }
+
+    fn fill_value(&self) -> FillValue {
+        FillValue::from(0u64)
+    }
+
+    fn dimension_names(&self) -> Option<Vec<DimensionName>> {
+        Some(vec![
+            DimensionName::new("Triples"),
+            DimensionName::new("Complementary fields"),
+        ])
+    }
+
+    fn array_to_bytes_codec(
+        &self,
+        _: &Dimensionality,
+    ) -> StorageResult<Box<dyn ArrayToBytesCodecTraits>> {
+        let mut sharding_codec_builder = ShardingCodecBuilder::new(vec![1, 3].try_into()?);
+        sharding_codec_builder.bytes_to_bytes_codecs(vec![Box::new(GzipCodec::new(5)?)]);
+        Ok(Box::new(sharding_codec_builder.build()))
+    }
+}
+
+impl LayoutOps<Chunk> for ComplementLayout {
+    fn graph_iter(&self, graph: Graph) -> Vec<Chunk> {
+        graph
+            .iter()
+            .enumerate()
+            .flat_map(|(first_term, triples)| {
+                triples
+                    .iter()
+                    .map(|&(second_term, third_term)| (first_term as u32, second_term, third_term))
+                    .collect::<Vec<Chunk>>()
+            })
+            .collect::<Vec<Chunk>>()
+    }
+
+    fn store_chunk_elements(&self, chunk: &[Chunk], _: usize) -> Vec<u64> {
+        let mut ans = Vec::new();
+        for &(first_term, second_term, third_term) in chunk {
+            ans.push(first_term as u64);
+            ans.push(second_term as u64);
+            ans.push(third_term as u64);
+        }
+        ans
+    }
+
+    fn retrieve_chunk_elements(
+        &mut self,
+        matrix: &Mutex<TriMat<usize>>,
+        first_term_index: usize, // TODO: will first_term_index instead of chunk[0] do the trick?
+        chunk: &[usize],
+    ) {
+        matrix
+            .lock()
+            .add_triplet(chunk[0], chunk[2], chunk[1] as usize);
+    }
+
+    fn sharding_factor(&self, dimensionality: &Dimensionality) -> usize {
+        dimensionality.first_term_size * dimensionality.third_term_size
+    }
+}
diff --git a/src/storage/layout/mod.rs b/src/storage/layout/mod.rs
index f21281b..c9b8b9b 100644
--- a/src/storage/layout/mod.rs
+++ b/src/storage/layout/mod.rs
@@ -28,6 +28,7 @@ type ArrayToBytesCodec = Box<dyn ArrayToBytesCodecTraits>;
 
 pub mod matrix;
 pub mod tabular;
+pub mod complement;
 
 pub trait LayoutOps<C> {
     fn retrieve_attributes(&mut self, arr: &Array<OpendalStore>) -> StorageResult<Dictionary> {
@@ -172,3 +173,20 @@ pub trait Layout<C>: LayoutOps<C> {
         dimensionality: &Dimensionality,
     ) -> StorageResult<ArrayToBytesCodec>;
 }
+
+
+pub trait ComplementaryLayout<C>: LayoutOps<C> {
+    fn shape(&self, dimensionality: &Dimensionality) -> Vec<u64>;
+    fn data_type(&self) -> DataType;
+    fn chunk_shape(
+        &self,
+        chunking_strategy: ChunkingStrategy,
+        dimensionality: &Dimensionality,
+    ) -> ChunkGrid;
+    fn fill_value(&self) -> FillValue;
+    fn dimension_names(&self) -> Option<Vec<DimensionName>>;
+    fn array_to_bytes_codec(
+        &self,
+        dimensionality: &Dimensionality,
+    ) -> StorageResult<ArrayToBytesCodec>;
+}