在SI疾病传播模型中，网络中的节点在任一时刻有两种可能的状态，易感态susceptible（S）和感染态infected（I）。处于易感态（S）的节点当被感染后转变为感染态（I）并且不能恢复。我们假设在t_0时刻网络中除了一个节点被感染了之外，这个节点就是传播源，其余的所有节点都处于易感态。之后传播源以一定的疾病传播概率（rates of infection）感染它的邻居，与此同时，疾病或者是信息开始在网络中传播。
SI传播模型的C语言实现（完整代码见下）
@sourceNode为疾病的传播源
@rateOfInfection为疾病的传播概率
思路：从传播源开始，对于该传播源的所有的邻居节点，以一定的概率将疾病传染给这些邻居节点。（在传播的时候，随机选择邻居进行传播而不是按照一定的顺序，例如节点的id）。然后统计网络中所有被疾病感染的节点，对于这些节点，随机依次的选择其中的节点作为“传播源”将疾病试图传染给自己未被感染的邻居。（同样在选择邻居进行传染的时候，也是随机的挑选邻居尝试传染）。
void SI(int sourceNode, double rateOfInfection) { int i, j; double probability_infected = 0.0; int clock = 1; int stop = 0; int I_nodes, S_neighbors, count1, count2,temp_I_array_length, temp_S_array_length; int rand_infected_node_index, rand_infected_node_id, rand_sus_node_index, rand_sus_node_id; I_nodes = S_neighbors = count1 = count2 = 0; int* I_node_array; int* S_neighbor_array; infected_sequences[sourceNode].S_or_I = infected_sequences[sourceNode].times = 1; infected_sequences[sourceNode].from = 0; while(1) { clock++; //记录感染时间 I_nodes = 0; //记录被感染的节点的个数 for( i = 1; i <= network_size; i++ ) if( infected_sequences[i].S_or_I ) I_nodes++; if( !(I_node_array = (int*)malloc(sizeof(int) * (I_nodes + 1))) ) { printf("malloc I_node_array* error\n"); exit(0); } count1 = 1; for( i = 1; i <= network_size; i++ ) if( infected_sequences[i].S_or_I ) I_node_array[count1++] = i; //构造已经被感染的节点的集合 temp_I_array_length = I_nodes; for( i = 1; i <= I_nodes; i++ ) { rand_infected_node_index = rand() % temp_I_array_length + 1; //随机选择已经感染的节点 rand_infected_node_id = I_node_array[rand_infected_node_index]; I_node_array[rand_infected_node_index] = I_node_array[temp_I_array_length--]; S_neighbors = 0; for( j = 1; j <= network_size; j++ ) //统计已感染节点的没有感染的邻居节点个数 if( adjacentMatrix[rand_infected_node_id][j] && !( infected_sequences[j].S_or_I ) ) S_neighbors++; if( S_neighbors == 0 ) continue; if( !(S_neighbor_array = (int*)malloc(sizeof(int) * (S_neighbors + 1))) ) { printf("malloc S_neighbor_array* error\n"); exit(0); } int count2 = 1; for( j = 1; j <= network_size; j++ ) if( adjacentMatrix[rand_infected_node_id][j] && !( infected_sequences[j].S_or_I ) ) S_neighbor_array[count2++] = j; temp_S_array_length = S_neighbors; for( j = 1; j <= S_neighbors; j++ ) { //随机选择没有感染的节点进行传播 rand_sus_node_index = rand() % temp_S_array_length + 1; rand_sus_node_id = S_neighbor_array[rand_sus_node_index]; S_neighbor_array[rand_sus_node_index] = S_neighbor_array[temp_S_array_length--]; probability_infected = (double)(rand() % 1000) / (double)1000; if( infected_sequences[rand_sus_node_id].S_or_I = probability_infected < rateOfInfection ? 1 : 0 ) { infected_sequences[rand_sus_node_id].times = clock; infected_sequences[rand_sus_node_id].from = rand_infected_node_id; } } free(S_neighbor_array); S_neighbor_array = NULL; } free(I_node_array); I_node_array = NULL; stop = 0; for( i = 1; i <= network_size; i++ ) stop += infected_sequences[i].S_or_I; if( network_size == stop ) break; } //可以输出到文件进行保存 //printf("SI process:\n"); //printf("node id :");for( i = 1; i <= network_size; i++ )printf("%5d", i);printf("\n"); //printf("node times:");for( i = 1; i <= network_size; i++ )printf("%5d", infected_sequences[i].times);printf("\n"); //printf("node from :");for( i = 1; i <= network_size; i++ )printf("%5d", infected_sequences[i].from);printf("\n"); } 使用gephi进行可视化
#include<stdio.h> #include<string.h> #include<stdlib.h> #include<time.h> int network_size; int edges_size; short** adjacentMatrix; double rateOfInfection; char filename[100]; typedef struct{ int S_or_I; //标记该节点是否被感染 int times; //记录该节点的感染时间 int from; //记录该节点的感染来源 }SI_Node; SI_Node* infected_sequences; void init(); void readNetworkAndTransformFormat(); void SI(int sourceNode, double rateOfInfection); void saveSIResult(); int main(int argc, char** argv) { if( argc != 6 ) { printf("This algorithm require 3 paramenters\n"); printf("\t1.network size(vertaies number)\n"); printf("\t2.edges size\n"); printf("\t3.propagation probability\n"); printf("\t4.file name contain edges information\n"); printf("\t5.the source node ID\n"); printf("\t\texample: a.exe 332 2126 0.5 edgesForSIModel.data 255\n"); exit(0); } srand((unsigned)time(NULL)); network_size = atoi(argv[1]); edges_size = atoi(argv[2]); rateOfInfection = atof(argv[3]); strcat(filename, argv[4]); int sourceID = atoi(argv[5]); printf("show information of input: network_size: %d,edges number: %d,propagation probability: %f,file name: %s, source node ID: %d\n", network_size, edges_size, rateOfInfection, filename, sourceID); init(); readNetworkAndTransformFormat(); SI(sourceID, rateOfInfection); saveSIResult(); return 0; } void init() { int i, j; if( !(adjacentMatrix = (short**)malloc(sizeof(short*) * (network_size + 1))) ) { printf("adjacentMatrix** malloc error"); exit(0); } for( i = 1; i <= network_size; i++ ) { if( !(adjacentMatrix[i] = (short*)malloc(sizeof(short) * (network_size + 1))) ) { printf("adjacentMatrix[%d]* malloc error"); exit(0); } } for( i = 1; i <= network_size; i++ ) for( j = 1; j <= network_size; j++ ) adjacentMatrix[i][j] = 0; if( !(infected_sequences = (SI_Node*)malloc(sizeof(SI_Node) * (network_size + 1))) ) { printf("infected_sequences* malloc error"); exit(0); } for( i = 1; i <= network_size; i++ ) infected_sequences[i].S_or_I = infected_sequences[i].times = infected_sequences[i].from = 0; } /* * 大多数的真实网络给出的形式为source target,在这里进行转化为邻接矩阵 * */ void readNetworkAndTransformFormat() { int i, j, source, target; source = target = 0; FILE* fread; if( NULL == (fread = fopen(filename, "r")) ) { printf("open file error"); exit(0); } for( i = 1; i <= edges_size; i++ ) { if( 2 != fscanf(fread, "%d %d", &source, &target) ) { printf("fscanf error: %d", i); exit(0); } adjacentMatrix[source][target] = adjacentMatrix[target][source] = 1; } fclose(fread); /* for( i = 1; i <= network_size; i++ ) { for( j = 1; j <= network_size; j++ ) printf("%d ", adjacentMatrix[i][j]); printf("\n"); } */ } /* * 使用SI模型进行传播 * */ void SI(int sourceNode, double rateOfInfection) { int i, j; double probability_infected = 0.0; int clock = 1; int stop = 0; int I_nodes, S_neighbors, count1, count2,temp_I_array_length, temp_S_array_length; int rand_infected_node_index, rand_infected_node_id, rand_sus_node_index, rand_sus_node_id; I_nodes = S_neighbors = count1 = count2 = 0; int* I_node_array; int* S_neighbor_array; infected_sequences[sourceNode].S_or_I = infected_sequences[sourceNode].times = 1; infected_sequences[sourceNode].from = 0; while(1) { clock++; //记录感染时间 I_nodes = 0; //记录被感染的节点的个数 for( i = 1; i <= network_size; i++ ) if( infected_sequences[i].S_or_I ) I_nodes++; if( !(I_node_array = (int*)malloc(sizeof(int) * (I_nodes + 1))) ) { printf("malloc I_node_array* error\n"); exit(0); } count1 = 1; for( i = 1; i <= network_size; i++ ) if( infected_sequences[i].S_or_I ) I_node_array[count1++] = i; //构造已经被感染的节点的集合 temp_I_array_length = I_nodes; for( i = 1; i <= I_nodes; i++ ) { rand_infected_node_index = rand() % temp_I_array_length + 1; //随机选择已经感染的节点 rand_infected_node_id = I_node_array[rand_infected_node_index]; I_node_array[rand_infected_node_index] = I_node_array[temp_I_array_length--]; S_neighbors = 0; for( j = 1; j <= network_size; j++ ) //统计已感染节点的没有感染的邻居节点个数 if( adjacentMatrix[rand_infected_node_id][j] && !( infected_sequences[j].S_or_I ) ) S_neighbors++; if( S_neighbors == 0 ) continue; if( !(S_neighbor_array = (int*)malloc(sizeof(int) * (S_neighbors + 1))) ) { printf("malloc S_neighbor_array* error\n"); exit(0); } int count2 = 1; for( j = 1; j <= network_size; j++ ) if( adjacentMatrix[rand_infected_node_id][j] && !( infected_sequences[j].S_or_I ) ) S_neighbor_array[count2++] = j; temp_S_array_length = S_neighbors; for( j = 1; j <= S_neighbors; j++ ) { //随机选择没有感染的节点进行传播 rand_sus_node_index = rand() % temp_S_array_length + 1; rand_sus_node_id = S_neighbor_array[rand_sus_node_index]; S_neighbor_array[rand_sus_node_index] = S_neighbor_array[temp_S_array_length--]; probability_infected = (double)(rand() % 1000) / (double)1000; if( infected_sequences[rand_sus_node_id].S_or_I = probability_infected < rateOfInfection ? 1 : 0 ) { infected_sequences[rand_sus_node_id].times = clock; infected_sequences[rand_sus_node_id].from = rand_infected_node_id; } } free(S_neighbor_array); S_neighbor_array = NULL; } free(I_node_array); I_node_array = NULL; stop = 0; for( i = 1; i <= network_size; i++ ) stop += infected_sequences[i].S_or_I; if( network_size == stop ) break; } //可以输出到文件进行保存 //printf("SI process:\n"); //printf("node id :");for( i = 1; i <= network_size; i++ )printf("%5d", i);printf("\n"); //printf("node times:");for( i = 1; i <= network_size; i++ )printf("%5d", infected_sequences[i].times);printf("\n"); //printf("node from :");for( i = 1; i <= network_size; i++ )printf("%5d", infected_sequences[i].from);printf("\n"); } /* * 用于gephi作图 * */ void saveSIResult() { int i, j; FILE *fNodeInfo, *fEdgeInfo; if( NULL == (fNodeInfo = fopen("nodeInfo.csv", "w")) ) { printf("nodeInfo.csv open error"); exit(0); } if( NULL == (fEdgeInfo = fopen("edgeInfo.csv", "w")) ) { printf("edgeInfo.csv open error"); exit(0); } //节点和节点的感染时间 fprintf(fNodeInfo, "id,label,color\n"); for( i = 1; i <= network_size; i++ ) fprintf(fNodeInfo, "%d,%d,%d\n", i, i, infected_sequences[i].times); fclose(fNodeInfo); fprintf(fEdgeInfo, "source,target\n"); for( i = 1; i <= network_size; i++ ) { for( j = i + 1; j <= network_size; j++ ) { if( adjacentMatrix[i][j] && infected_sequences[i].from == j ) { //printf("%d --> %d\n",j, i); fprintf(fEdgeInfo, "%d,%d\n", j, i); }else if( adjacentMatrix[i][j] && infected_sequences[j].from == i ) { //printf("%d --> %d\n", i, j); fprintf(fEdgeInfo, "%d,%d\n", i, j); }else if( adjacentMatrix[i][j] ) { //printf("%d --- %d\n", i, j); fprintf(fEdgeInfo, "%d,%d\n", i, j); } } } fclose(fEdgeInfo); }
代码中使用了USArir网络（美国航空网络,数据下载地址：http://vlado.fmf.uni-lj.si/pub/networks/data/mix/USAir97.net）。原网络为含权网路，包含332个机场和2126条航线。
下图为使用gephi可视化该网络的结果。
运行以上代码，通过输出的csv文件，可以绘制出疾病传播的趋势，黄色的节点为传播源，深红到深蓝的渐变表示感染时间的增加。即越红的节点表示越早感染，越蓝的节点表示该节点越晚被感染。
如果只是保留有疾病传播的路径那么可以得到下图
