diff --git a/src/graph/Makefile b/src/graph/Makefile
index 9bc0a2c4..ba156b5f 100644
--- a/src/graph/Makefile
+++ b/src/graph/Makefile
@@ -14,7 +14,7 @@ INCLUDE := -I../ -L../list/single  -L../hash-table -L../set -L../queue -L../stac
 
 # targets to compile
 TEST_TARGET = test
-TARGETS = graph.o bfs.o dfs.o acyclical.o tarjan.o dijkstra.o kruskal.o
+TARGETS = graph.o bfs.o dfs.o acyclical.o tarjan.o dijkstra.o kruskal.o prim.o
 LIBRARY_OBJS = $(TARGETS)
 
 TEST_BINARY = $(TEST_TARGET).$(EXTENSION)
diff --git a/src/graph/graph.c b/src/graph/graph.c
index 649d2ae1..1eb19b00 100644
--- a/src/graph/graph.c
+++ b/src/graph/graph.c
@@ -131,7 +131,38 @@ List* graph_edges_ordered(Graph *g) {
     }
 
     return edges_ordered;
+}
+
 
+List* graph_remove_duplicated_edges(List* edges) {
+    List *node = edges;
+    while (node != NULL) {
+        int u = node->key;
+        int v = node->data;
+        edges = list_remove_by_key_data(edges, v, u);
+        node = node->next;
+    }
+    return edges;
+}
+
+int graph_edges_sum(Graph *g) {
+    int s = 0;
+    List *edges = graph_edges(g);
+
+    if (!g->directed) {
+        edges = graph_remove_duplicated_edges(edges);
+    }
+
+    Iterator *it = list_iterator(edges);
+    while (!iterator_done(it)) {
+        List *node = (List*) iterator_next(it);
+        int u = node->key;
+        int v = node->data;
+        s += graph_get_edge_weight(g, u, v);
+    }
+    list_free(edges);
+    iterator_free(it);
+    return s;
 }
 
 size_t graph_size(Graph *g) {
@@ -232,6 +263,12 @@ bool graph_has_edge(Graph *g, int u, int v) {
     return set_contains(set_u, v);
 }
 
+bool graph_has_node(Graph *g, int u) {
+    bool exists;
+    hash_table_gen_get(g->adj, u, &exists);
+    return exists;
+}
+
 Set* graph_get_neighbors(Graph *g, int node) {
     bool exists;
     Set *neighbors = (Set*) hash_table_gen_get(g->adj, node, &exists);
@@ -257,6 +294,7 @@ void graph_print(Graph *g) {
     Iterator *it = graph_nodes_iterator(g);
     while(!iterator_done(it)) {
         int u = *(int*)iterator_next(it);
+        printf("%d: ", u);
         Set *neighbors = (Set*) hash_table_gen_get(g->adj, u, NULL);
         if (g->tarjan) {
             Iterator *neighbors_it = set_iterator_items(neighbors);
diff --git a/src/graph/graph.h b/src/graph/graph.h
index 217889e1..46c3d785 100644
--- a/src/graph/graph.h
+++ b/src/graph/graph.h
@@ -145,6 +145,15 @@ void graph_remove_node(Graph *g, int node);
  */
 bool graph_has_edge(Graph *g, int u, int v);
 
+/**
+ * @brief Checks if a node exists in the graph.
+ * @param g The graph.
+ * @param u The node.
+ * @return True if the node exists, false otherwise.
+ * @ingroup DataStructureMethods
+ */
+bool graph_has_node(Graph *g, int u);
+
 /**
  * @brief Gets the neighbors of a node.
  * @param g The graph.
@@ -215,6 +224,13 @@ List* graph_edges(Graph *g);
  */
 List* graph_edges_ordered(Graph *g);
 
+/**
+ * @brief Sum of the edge weights. If undirected, calculate (u, v) == (v, u) only once.
+ * @param g The graph to traverse.
+ * @ingroup DataStructureMethods
+ */
+int graph_edges_sum(Graph *g);
+
 /**
  * @brief Get the maximum node id on the graph.
  * @return maximum node id on the graph.
@@ -274,13 +290,22 @@ List* graph_topological_sort(Graph *g);
 Graph* graph_dijkstra(Graph* g, int source);
 
 /**
- * @brief Run kruskal algorithm to get the minimum-span tree.
+ * @brief Run Kruskal algorithm to get the minimum-span tree.
  * @param g The graph to traverse.
  * @return a new graph with the minimum span tree.
  * @ingroup DataStructureMethods
  */
 Graph* graph_kruskal(Graph* g);
 
+/**
+ * @brief Run Prim algorithm to get the minimum-span tree.
+ * @param g The graph to traverse.
+ * @param start Initial node to start.
+ * @return a new graph with the minimum span tree.
+ * @ingroup DataStructureMethods
+ */
+Graph* graph_prim(Graph* g, int start);
+
 /**
  * @brief Run dijkstra algorithm and calculate the minimum distance.
  * @param g The graph to traverse.
diff --git a/src/graph/kruskal.c b/src/graph/kruskal.c
index 579d2c2e..f0b26b89 100644
--- a/src/graph/kruskal.c
+++ b/src/graph/kruskal.c
@@ -2,7 +2,7 @@
 #include "../set/set-disjoint.h"
 
 Graph* graph_kruskal(Graph *g) {
-    Graph *g_kruskal = graph_create();
+    Graph *g_kruskal = graph_undirected_create();
     DisjointSet *components = set_disjoint_create(graph_max_node_id(g) + 1);
     List *edges = graph_edges_ordered(g);
     Iterator *it = list_iterator(edges);
diff --git a/src/graph/prim.c b/src/graph/prim.c
new file mode 100644
index 00000000..a92100b5
--- /dev/null
+++ b/src/graph/prim.c
@@ -0,0 +1,46 @@
+#include "graph.h"
+#include "../utils/pair_hash.h"
+#include "../pqueue/pqueue.h"
+
+void update_heap(Graph* g, PQueue* pq, Set* visited, int start) {
+    Set* neighbors = graph_get_neighbors(g, start);
+    Iterator *it = set_iterator_items(neighbors);
+    while (!iterator_done(it)) {
+        List *neighbor_weight = (List*) iterator_next(it);
+        if (!set_contains(visited, neighbor_weight->key)) {
+            int k = pair_hash(start, neighbor_weight->key);
+            int w = neighbor_weight->data;
+            pqueue_insert(pq, k, w);
+        }
+    }
+    set_free(neighbors);
+    iterator_free(it);
+}
+
+// WARNING: this implementation only return the Minimum Spanning Tree
+// of conected component from <start> node. If some node is
+// unreachable from <start> will be not included in the final tree.
+Graph* graph_prim(Graph *g, int start) {
+    Graph* g_prim = graph_undirected_create();
+    Set* visited = set_create();
+    PQueue *pq = pqueue_create(MIN_PQUEUE);
+    update_heap(g, pq, visited, start);
+    set_add(visited, start);
+
+    while (!pqueue_is_empty(pq)) {
+        PQueueNode node = pqueue_extract(pq);
+        int u = unpair_hash_x(node.key);
+        int v = unpair_hash_y(node.key);
+        int w = node.value;
+        if (set_contains(visited, v)) {
+            continue;
+        }
+        graph_add_edge_with_weight(g_prim, u, v, w);
+        set_add(visited, v);
+        update_heap(g, pq, visited, v);
+    }
+    pqueue_free(pq);
+    set_free(visited);
+
+    return g_prim;
+}
diff --git a/src/graph/tarjan.c b/src/graph/tarjan.c
index df53c0c3..a87e2679 100644
--- a/src/graph/tarjan.c
+++ b/src/graph/tarjan.c
@@ -12,7 +12,7 @@ struct TarjanContext {
 };
 
 void free_tarjan_context(struct TarjanContext *tc) {
-    // keep on memor: g_tarjan + componentes
+    // keep on memory: g_tarjan + components
     free(tc->exploration);
     free(tc->complete);
     stack_free(tc->path);
diff --git a/src/graph/test.c b/src/graph/test.c
index fe862fcc..679f8a4e 100644
--- a/src/graph/test.c
+++ b/src/graph/test.c
@@ -204,7 +204,7 @@ void test_graph_edges_ordered() {
     graph_add_edge_with_weight(g, 2, 3, 10);
     graph_add_edge_with_weight(g, 1, 2, 7);
     graph_add_edge_with_weight(g, 1, 3, 9);
-    printf(":: graph");
+    printf(":: graph\n");
     graph_print(g);
 
 
@@ -389,9 +389,11 @@ void test_graph_dijkstra(bool extra_tests) {
     graph_free(dijkstra_result);
 }
 
-void test_graph_kruskal() {
+void test_graph_kruskal(bool extra_tests) {
+    char cwd[PATH_MAX];
+    getcwd(cwd, sizeof(cwd));
     puts("== Graph kruskal test");
-    Graph *g = graph_create();
+    Graph *g = graph_undirected_create();
     graph_add_edge_with_weight(g, 1, 2, 10);
     graph_add_edge_with_weight(g, 1, 3, 20);
     graph_add_edge_with_weight(g, 2, 3, 5);
@@ -402,14 +404,57 @@ void test_graph_kruskal() {
     printf(":: input graph\n");
     graph_print(g);
 
-    printf(":: kruskal tree\n");
+    printf(":: kruskal minimum spanning tree\n");
     Graph *g_kruskal = graph_kruskal(g);
     graph_print(g_kruskal);
 
+    if (extra_tests) {
+        graph_export_to_dot(g, "test_graph_kruskal_input.dot");
+        printf("saved input: %s/test_graph_kruskal_input.dot\n", cwd);
+        graph_export_to_dot(g_kruskal, "test_graph_kruskal_output.dot");
+        printf("saved output: %s/test_graph_kruskal_output.dot\n", cwd);
+    }
+
+    int s = graph_edges_sum(g_kruskal);
+    printf("Cost sum: %d\n", s);
+    assert(s == 31);
     graph_free(g);
     graph_free(g_kruskal);
 }
 
+void test_graph_prim(bool extra_tests) {
+    char cwd[PATH_MAX];
+    getcwd(cwd, sizeof(cwd));
+    puts("== Graph prim test");
+    Graph *g = graph_undirected_create();
+    graph_add_edge_with_weight(g, 1, 2, 10);
+    graph_add_edge_with_weight(g, 1, 3, 20);
+    graph_add_edge_with_weight(g, 2, 3, 5);
+    graph_add_edge_with_weight(g, 3, 4, 30);
+    graph_add_edge_with_weight(g, 4, 1, 9);
+    graph_add_edge_with_weight(g, 5, 1, 7);
+
+    printf(":: input graph\n");
+    graph_print(g);
+
+    printf(":: prim minimum spanning tree\n");
+    Graph *g_prim = graph_prim(g, 5);
+    graph_print(g_prim);
+
+    if (extra_tests) {
+        graph_export_to_dot(g, "test_graph_prim_input.dot");
+        printf("saved input: %s/test_graph_prim_input.dot\n", cwd);
+        graph_export_to_dot(g_prim, "test_graph_prim_output.dot");
+        printf("saved output: %s/test_graph_prim_output.dot\n", cwd);
+    }
+
+    int s = graph_edges_sum(g_prim);
+    printf("Cost sum: %d\n", s);
+    assert(s == 31);
+    graph_free(g);
+    graph_free(g_prim);
+}
+
 
 bool should_run_extra_tests(int argc, char *argv[]) {
     // Iterate through the command-line arguments starting from argv[1]
@@ -434,7 +479,8 @@ int main(int argc, char *argv[]) {
     test_graph_topological_sort();
     test_graph_dijkstra(extra_tests);
     test_graph_edges_ordered();
-    test_graph_kruskal();
+    test_graph_kruskal(extra_tests);
+    test_graph_prim(extra_tests);
     if (should_run_extra_tests(argc, argv)) {
         test_graph_export();
     }
diff --git a/src/list/single/list.c b/src/list/single/list.c
index 6fc8d484..12821d9e 100644
--- a/src/list/single/list.c
+++ b/src/list/single/list.c
@@ -255,6 +255,19 @@ List* list_remove(List *l, int data) {
     return l;
 }
 
+List* list_remove_by_key_data(List *l, int key, int data) {
+    if (!list_empty(l)) {
+        if (l->key == key && l->data == data) {
+            List* next = l->next;
+            free(l);
+            l = next;
+        } else {
+            l->next = list_remove_by_key_data(l->next, key, data);
+        }
+    }
+    return l;
+}
+
 List* list_remove_by_key(List *l, int key){
     if (!list_empty(l)) {
         if (l->key == key) {
diff --git a/src/list/single/list.h b/src/list/single/list.h
index 40ca2308..fac18421 100644
--- a/src/list/single/list.h
+++ b/src/list/single/list.h
@@ -170,6 +170,17 @@ List* list_remove(List *l, int data);
  */
 List* list_remove_by_key(List *l, int key);
 
+
+/**
+ * @brief Remove specific element from List by a key equal data
+ * @param l List to remove with \p key
+ * @param key integer value to remove
+ * @param data integer value to remove
+ * @return new list without the node which contains \p key and \p data
+ * @ingroup DataStructureMethods
+ */
+List* list_remove_by_key_data(List *l, int key, int data);
+
 /**
  * @brief Free memory of List and its nodes
  * @ingroup DataStructureMethods
diff --git a/src/pqueue/pqueue.c b/src/pqueue/pqueue.c
index f8dff4e9..f7d0ad3f 100644
--- a/src/pqueue/pqueue.c
+++ b/src/pqueue/pqueue.c
@@ -87,11 +87,11 @@ void min_heapify(PQueue *pq, int i) {
 
 PQueue* pqueue_create(PQueueType type) {
     PQueue* pq = (PQueue*) malloc(sizeof(PQueue));
-    pq->index = hash_table_create(PQUEUE_SIZE * 10);
     if (pq == NULL) {
         perror("Failed to allocate memory for PQueue");
         exit(EXIT_FAILURE);
     }
+    pq->index = hash_table_create(PQUEUE_SIZE * 10);
     pq->heap = (PQueueNode*) malloc(PQUEUE_SIZE * sizeof(PQueueNode));
     if (pq->heap == NULL) {
         perror("Failed to allocate memory for PQueue heap");
diff --git a/src/utils/pair_hash.h b/src/utils/pair_hash.h
new file mode 100644
index 00000000..ba2c0773
--- /dev/null
+++ b/src/utils/pair_hash.h
@@ -0,0 +1,31 @@
+#include <math.h>
+
+/* @brief Pair function of Szudzik (2006).
+ * @details Useful to encapsulate two integers as a unique reversible integer hash.
+ * @return hashed integer.
+ * @see https://en.wikipedia.org/wiki/Pairing_function#Cantor_pairing_function
+ */
+static inline int pair_hash(int x, int y) {
+    if (x < y) {
+        return y * y + x;
+    }
+    return x * x + x + y;
+}
+
+static inline int unpair_hash_x(int z) {
+    int z_sqrt = floor(sqrt(z));
+    int z_rest = z - z_sqrt * z_sqrt;
+    if (z_rest < z_sqrt) {
+        return z_rest;
+    }
+    return z_rest;
+}
+
+static inline int unpair_hash_y(int z) {
+    int z_sqrt = floor(sqrt(z));
+    int z_rest = z - z_sqrt * z_sqrt;
+    if (z_rest < z_sqrt) {
+        return z_sqrt;
+    }
+    return z_rest - z_sqrt;
+}