diff --git a/test/test_network.cpp b/test/test_network.cpp
index 47a0076..36f9fc8 100644
--- a/test/test_network.cpp
+++ b/test/test_network.cpp
@@ -19,23 +19,41 @@ TEST_CASE( "Testing the network class" )
     // Does n_agents work?
     REQUIRE( network->n_agents() == n_agents );
 
+    // Check that the function for setting neighbours and a single weight work
+    // Agent 3
+    std::vector<size_t> buffer_n_get{};                       // buffer for getting neighbours
+    std::vector<Seldon::Network::WeightT> buffer_w_get{};     // buffer for getting the weights
+    std::vector<size_t> neigh{ { 0, 10 } };                   // new neighbours
+    std::vector<Seldon::Network::WeightT> weight{ 0.5, 0.5 }; // new weights (const)
+    network->set_neighbours_and_weights( 3, neigh, 0.5 );
+    network->get_weights( 3, buffer_w_get );
+    REQUIRE_THAT( buffer_w_get, Catch::Matchers::UnorderedRangeEquals( buffer_w_get ) );
+
     // Change the connections for agent 3
-    std::vector<size_t> buffer_n{ { 0, 10, 15 } };
-    std::vector<Seldon::Network::WeightT> buffer_w{ 0.1, 0.2, 0.3 };
+    std::vector<size_t> buffer_n{ { 0, 10, 15 } };                   // new neighbours
+    std::vector<Seldon::Network::WeightT> buffer_w{ 0.1, 0.2, 0.3 }; // new weights
     network->set_neighbours_and_weights( 3, buffer_n, buffer_w );
 
     // Make sure the changes worked
-    std::vector<size_t> buffer_n_get{};
-    std::vector<Seldon::Network::WeightT> buffer_w_get{};
     network->get_neighbours( 3, buffer_n_get );
     network->get_weights( 3, buffer_w_get );
 
     REQUIRE_THAT( buffer_n_get, Catch::Matchers::UnorderedRangeEquals( buffer_n ) );
     REQUIRE_THAT( buffer_w_get, Catch::Matchers::UnorderedRangeEquals( buffer_w ) );
 
+    // Check that the push_back function works for agent 3
+    buffer_n.push_back( 5 );                              // new neighbour
+    buffer_w.push_back( 1.0 );                            // new weight for this new connection
+    network->push_back_neighbour_and_weight( 3, 5, 1.0 ); // new connection added with weight
+    // Check that the change worked for the push_back function
+    network->get_neighbours( 3, buffer_n_get );
+    network->get_weights( 3, buffer_w_get );
+    REQUIRE_THAT( buffer_n_get, Catch::Matchers::UnorderedRangeEquals( buffer_n ) );
+    REQUIRE_THAT( buffer_w_get, Catch::Matchers::UnorderedRangeEquals( buffer_w ) );
+
     // Now we test the transpose() function
 
-    // First record all the old edges as tupels (i,j,w) where this edge goes from j -> i with weight w
+    // First record all the old edges as tuples (i,j,w) where this edge goes from j -> i with weight w
     std::set<std::tuple<size_t, size_t, Network::WeightT>> old_edges;
     for( size_t i_agent = 0; i_agent < network->n_agents(); i_agent++ )
     {